If this wasn't a thing, what did naval battles of say, the 100 Years War look like? Was it like earlier naval combat, where it was mostly about ramming and boarding actions?
It's hard to generalize naval action in the medieval period as a whole, because it encompasses such a wide range of circumstances, strategies, engineering elements, and doctrines that vary from place to place and from time to time; the battle of Sandwich in 1217, for instance, bears little resemblance to earlier phases of northern European sea and riverborne raids, and would also differ starkly from an engagement like Lepanto in 1571.
But since you're specifically asking about naval warfare in the cross-channel engagements of the Hundred Years War we can be a little more specific! First we should talk a bit about the ships and ship-building, then the tasks expected of a squadron of ships in aid of military operations on land, and lastly on some examples of actual engagements.
Ships and Ship-building
Trade and travel connected the British isles and the English channel with traffic from all around Europe, and as such there was a large diversity of ship types and purposes. Round ships or nefs were common in the 13th and 14th centuries, built initially in France and serving primarily as transport and trade vessels. They were predominantly sail-powered, and often supported fore and aft castles if they had been built for or converted to use in war.
Nefs were similar to other, similar vessels, sail-powered trade and transport craft like cogs and carracks. The terms are sometimes interchanged and there's not necessarily a clear difference between many of them. Their construction, cross-sections, purpose, and handling were largely similar, but of course would have varied by regional practice and method of construction. But this is at least one broad category of the types of ships in use during the Hundred Years War; sail-powered cargo ships that could be converted to troop ships with the installation of fore and aft castles.
The other broad category was the galley. Oar-powered with sails that could be raised or lowered, galleys were predominantly used in the Mediterranean, but could be hired in for special purposes. The French hired twelve Genoese galleys to assist their Spanish and French fleet to support its efforts against Flanders in 1304. Galleys often carried rams, but were also equipped with fighting decks or truncated fore and aft castles as well. They were more maneuverable, but much more expensive to operate, as the rowers needed pay and food, and were far more numerous than the crews of nefs.
Building ships was a large and complicated undertaking, and organizing shipbuilding for a war was even more so. To organize, combine, man, supply and actually sail the fleet required a great deal of luck and logistical skill. Ships built primarily as fighting ships were often designated as "royal" vessels and were built and manned at the expense of the crown, but this was a rarified element of most battle fleets. Instead, a form of impressment was more common; the direct hiring or forced seizure of ships and crews in times of need. The History of William Marshal recounts that William had to win them over "with words and gifts and promises of rich rewards, till they were all fired with a fierce, brave will to go and engage the French" when their vessels were impressed into the fleet that eventually won the famous battle of Sandwich in 1217 (the history also repeatedly emphasizes how unhappy these pressed men were, and how many promises of booty Marshal had to make to keep them motivated).
In any case, both marshalling a fleet - that is, getting it together, armed, supplied, and waiting on favorable winds to sail - and building one were time-consuming and complicated, and this also meant that there was opportunity for raid, counter-raid, and what later might be called "cutting out expeditions;" small engagements of few ships with particular purposes of destroying materiel, or sinking and capturing ships. Piracy was also a concern, but one of the overriding concerns of naval operations in this period was the weather.
Banal as it sounds, weather was king. Unfavorable winds could leave whole fleets trapped in ports or along the coast for weeks, and whole seasons could come and go without a chance to go. Infamously, a storm had wrecked the White Ship (or, in French, Le Blanche-nef) in 1120, ushering in the Anarchy, killing nearly 300 people, including the heir of Henry I. Even oar-power wasn't reliable enough to conduct any large-scale operations when the weather was against the effort, and this is one of the primary reasons that large-scale naval battles tended to be the exception rather than the rule.
The role of ships
Though it sounds rather unglamorous, most of the duty of a ship in this period was aiding forces on land. Ferrying men, horses, and supplies, and contributing to a continuing line of resupply. Armies are complicated, and even what we might consider modest or small armies require an enormous amount of supplementary equipment, weapons and ammunition, food, and fresh water. Ships were also important in maintaining sieges on cities with access to rivers or seaports. The battle with the French mentioned above, Zierikzee in 1304, took place in a riverway near a city under siege.
With the emphasis on cargo load, rather than fighting power, it makes sense that we don't see a lot of reference to stone-throwing machines or artillery. The castles at the prow and stern were typically loaded with archers or crossbowmen and other men-at-arms, whose job it was to board or repel boarders when ships came to grapple in the rare event of a battle at sea. Otherwise, the job of ships was fetching and carrying, with the occasional opportunistic raid. In dire straits, such as when William Marshal impressed the coastal mariners for the battle of Sandwich, hasty emergency fleets were organized to oppose or obstruct an enemy fleet, but that was, as we've seen, quite rare.
I'll post a follow up below, describing some actions and listing my sources but for now I have to step away from the computer
Although not late medieval (which is usually what these fantasy stories base their general understanding of the medieval world on) in the section on the Expedition(s) to Crete in the De Ceremoniis of the Roman ("Byzantine") Emperor Constantine VII, he explicitly details the equipping of ships with artillery and flamethrowers:
For fitting out 4 traction-powered stone-throwers, 4 lambda-framed stone-throwers, 4 machines:
30 rings, 15 clamps, 30 shackles, also for the large bow-ballistae, rams for the tortoises, 15 bolts, 20 large weights, and 30 smaller weights, and for the large bow-ballistae the prescribed amount of iron. 10,000 litrai of pitch, 300 round pitchers of liquid tar, 40 pitchers of cedar resin, 8000 litrai of linen, 2000 litrai of hemp, 20 skiffs, 12 iron slings, 50 extra anchor cables, 50 anchors, 100 linden cables, 100 grapnel cables, 100 spartum cables, 200 lightweight cables, 100 four-legged grates, 50 litrai of linen for the sponges, 400 mooring cables, 24 siphons for the 8 pamphyloi, 80 siphons for the 40 ousakia khelandia, 6000 decking nails.
This is not the only source, as Emperor Leo VI's Taktike Constitution 19 also gives details:
By all means, it should have a siphon, bound in bronze, and placed up front on the prow, as is customary, so that it can project the prepared fire against the enemy. Above this particular siphon there should be a sort of platform made of planks and walled around by planks. Station combat troops there to ward off attacks coming from the prow of the enemy ships or to shoot whatever weapons they may choose against the whole enemy ship.
On the largest dromons erect the so-called xylokastra (forecastles) with their wall of planks somewhere around the middle of the mast. From these vantage points our men will shoot millstones or heavy pieces of iron such as those shaped like spathia (swords). These will either break up the enemy ship or, landing with great force, crush those on whom they fall. The men may also hurl other things capable of setting the enemy ships on fire or of killing the troops on board.
The ancients, as well as more recent authorities, devised many weapons for use against enemy ships and against the fighting men in them, such as prepared fire with thunder and fiery smoke discharged through the siphons, blackening them with smoke.
Or toxovolistrai placed in both the prow and the stern and on the two sides of the dromon, discharging small arrows that are called muias ("flies"). Still, others conceived of animals shut up in pots to be hurled against the enemy ships. Among these would be snakes, vipers, lizards, scorpions, and other such venomous creatures. When the pots are shattered, the animals bite and by their poison wipe out the enemy on board the ships.
And other pots filled with unslaked lime. When these are hurled and shattered, the vapor from the asvestos chokes and blinds the enemy and proves to be a huge annoyance.
Iron trivoloi (caltrops) hurled onto the enemy ships will cause them no little annoyance and will keep them from dutifully engaging in the battle at hand.
but we command that the pots full of the prepared fire, according to the prescribed method of their preparation, should be hurled; on shattering they shall easily burn up the ships of the enemy.
Make use also of the other method, that is, of the small siphons projected by hand from behind the iron skoutaria (shields) held by the soldiers. These are called kheirosiphone and have been fabricated recently by our majesty. These too will throw the prepared fire into the face of the enemy.
Also larger iron caltrops or sharp nails hammered into wooden spheres, then wrapped in hemp or some other substance, set on fire, and thrown against the enemy. Falling in various places, they will set the ships aflame.
It is possible to use the so-called cranes or similar gamma-shaped contrivances that revolve in a circle. When the enemy ships are bound to your dromons, turn the machine around against them and pour on them either burning liquid pitch or a net or some other material.
There were three kinds of machine artillery used by the Romans against enemy ships: the toxobolistra ("bow-ballista", still the classic torsion-powered engine seen in the classical and late antique Roman empire), the manganikon or alakation/elakation ("machine" or "revolver" aka a mangonel aka a traction trebuchet). These were slightly more complex than the typical machines we see in art or reconstructions, as they had pulleys as mentioned in the De Ceremoniis. These were what were used to hurl the aforementioned stones, fire grenades, and other more exotic ammunition, alongside with those hurled by hand. Finally there were the cranes, which had the same general form and function as the alakation but were used to swivel and pour or drop fire, stones, and nets directly onto the enemy watercraft.
It's also possible that the old onager, which would have simply been called a bolistra (it operates exactly the same way as bolt-thrower, but has one torsion spring which is positioned horizontally) was still around and also used to hurl small pots and anti-personnel stones. It is not directly mentioned as being mounted on the ships (just like the manganikon or alakation/elakation), but we know they were still around from various sources.
And of course, there was the siphon, the great invention of the 670's that allowed the Roman navy (which effectively hadn't had to deal with decked warship combat in ~600-700 years and learned that lesson the hard way after their open-decked patrol boats were smashed to pieces at the Battle of the Masts in 654) to use liquid fire to overpower the Arabs (the liquid fire itself wasn't a new invention, the siphon was).
As far as I know, most of this technology was eventually copied by the Western Europeans, as they brought back the counterweight trebuchet (invented by the Romans in the 1000's) after the first crusade, and the ballista was adapted into the springald. But I hope u/partymoses below can provide more information on that.
I hope this helps!
/u/PartyMoses has provided an excellent answer about naval warfare in general and what use of artillery there was, so I'm going to take the opportunity to briefly discuss what kinds of naval artillery existed during the early stages of the Hundred Years War and how they might have been used in battle.
To begin with, many French ships, at least, appear to have carried a "arbalète à 2 pieds" ("crossbow of two feet"). A 1253 statute from Marseille requires all ships with a cargo capacity of 2000 quintals or more (approximately 82 metric tonnes) two have two of these crossbows, and men who could use them, while ships of 4000 quintals (~164 tonnes) were requires to carrying an "arbalète à tour" (windlass crossbow) in addition to the two large crossbows. We also see this demonstrated in many of the ships involved in the battle of Sluys in 1340, with many of the smaller ships being equipped with 5-6 crossbows of one foot, one crossbow of two feet and a "garroc".
We don't exactly know what a crossbow of two feet was, as medieval authors assumed everyone knew what they meant, but my personal view is that in France (at least) the "arbalète à 2 pieds" was a large crossbow with a lathe approximately 120-130cm long, much like the Berkhamsted and Glasgow crossbows, and the need to span it with both feet on the ground probably resulted in the "two feet" moniker. These would have been bulky, awkward weapons likely at the maximum draw weight for belt and hook spanned crossbows, and thus much slower to shoot than regular crossbows.
How these were used is not entirely clear beyond the fact that they were regarded as a form of light artillery. It's plausible that they were used to shoot single, accurate shots designed to pierce heavy armour or shields and wound critical personnel. One 13th century chronicle, speaking of a siege, suggests that the bolt of a crossbow of two feet was capable of killing a man after penetrating window shutters, so it's not hard to imagine something similar occurring through a shield.
The smaller ships at Sluys also had, in addition to one and two foot crossbows, what was called a "garroc". Beyond the fact that it was a kind of crossbow, it's very hard to say exactly what a "garroc" was, and no universal definition exists to my knowledge, but I believe that it was a large crossbow too powerful to be spanned by hand and instead a "haussepied" - another obscure term, but I base my interpretation on the haussepied hunting trap in addition to some textual evidence (such as a 1359 Mallorcan document speaking of 12 "ballestes de leva") - was used. These were probably shooting bolts in excess of 200 grams weight, making them quite terrifying weapons. Again, these were probably used to try and punch through shields, armour or the wood of the ship's "castles". Possibly, although the evidence for this is very scant, they might even have been used to send fire bolts into the rigging of enemy ships.
A third sort of weapon used at Sluys was the "arbalète à tour", or windlass crossbow. They most likely resembled something like this, but with a winch and pulley system in most cases rather than a screw (which may have been a particularly English method of spanning them). These are getting closer to what people imagine when they think of siege engines mounted on a ship, and it's likely that they would have been used in a similar manner to springalds were at Sluys, which is to say they would have targeted the rigging in an attempt to destroy it and make the ship incapable of movement. I'm unsure whether the English had any of this type of weapon at Sluys, as my paleography is abysmal and the best sources remain unpublished.
Finally, we come to the "springald", which could mean a torsion power siege engine but also blended into the category of arbalète à tour. The English, based on what records we have, had about 11 of these at Sluys, while the French had an unknown number as are recorded as having been issued in 1340, although at least four were present, one on each of the Genoese galleys. They had been issued in small numbers over previous years, including two that were referred to as "small", so they were likely the least common naval weapon. At Sluys they only achieved one known success, destroying the rigging of the La Oliver, but it's likely they caused other, less notable, damage to ships and men. At the very least, they would have put a bolt through shield and plate deep enough to kill a man, which must have been unnerving to see happen.
Outside of the context of Sluys, we have less accurate records, but they remain present in naval warfare. At Calais, according to Jean le Bel, they were used onboard ships both to blockade the port and to act as ship to land artillery along Philip VI's path to the Edward's camp, while at Winchelsea in 1350 they caused serious casualties among the English until the distance was closed and they could no longer effectively target the smaller, lower English vessels. The Castilian ships also seem to have carried traction trebuchets, much as the Genoese and Pisans did in the 13th century and the Byzantines in the 10th, although I don't believe these were ever particularly common in the Atlantic. Some forms of artillery were definitely mounted
On the whole, then, while a great variety of heavy crossbows and mounted siege engines were employed onboard ships during the HYW, even the gunpowder artillery, was primarily used as anti-personnel weapons or to try and disable the ship via the rigging rather than by attempting to sink the ship. Most of the fighting was done at range by crossbowmen or archers, usually in the castles fore and aft, and by men at arms up close.
Bibliography
In addition to PartyMoses' books, I consulted:
