In 1338, the Battle of Arnemuiden took place, involving 5 English ships going up against a significantly larger French fleet.
One of the English ships, the Christopher, was equipped with 3 cannons and one hand cannon.
The English lost and the Christopher was captured.
The wikipedia article on this battle is extremely sparse and has almost no information.
How successful was the Christopher prior to the surrender? Are there any French records of going up against naval cannons for the first time? Were the French aware they would be fighting such a high tech ship?
Were there any battles in the war following this where ships equipped with gunpowder cannons went up against a fleet without these weapons, or did both sides quickly arm their ships with cannons?
The Battle of Arnemuiden is notable only because the English ships (probably) had some small cannons; the five cogs in the harbor, carrying a load of wool, were overwhelmed and captured by a raiding squadron of Franco-Genoese galleys. The Franco-Genoese squadron actually raided all up and down the Narrow Seas at the start of the Hundred Years War, spreading widespread panic in England, but that's not what you asked about.
The cannons on board the English ships bore no resemblance to the cannons that started to be widely used in the 16th century -- in fact, the first time we have evidence of heavy artillery being mounted aboard ships was in the Scottish navy, not otherwise notable for its naval innovation.
I wrote about this in this older answer. To quote from that a bit:
Anyhow, Arnemuiden might be the first battle with guns, or might not be; the evidence on either side is really sketchy. We know that the English "king's ship" All Hallows Cog was equipped with "a certain iron instrument for firing quarrels and lead pellets with powder, for the defence of the ship" (Rodger, Safeguard of the Sea p. 163) in 1338, but that was certainly an antipersonnel weapon not one that was aimed at destroying ships. Guns seem to have continued being very small in Europe for at least a century or so; when Sir Robert Clifford became Master of the Ordnance in 1496, he had a stock of 63 guns and 406 barrels of powder, as compared to 9,253 bows and 27,804 sheaves of arrows. What really brought about a revolution in gunnery warfare was happening in the Mediterranean, where the Venetians started mounting large guns right in the bows of a galley in the 1470s.
Interestingly, it seems to have been Scotland (not a notable naval power) where we first see heavy guns mounted on ships in northern Europe. James IV mounted several heavy guns in one or more of his ships during his war with Donald Dubh MacDonald beginning in 1504; in 1506 the castle of Stornoway was battered into submission. It seems likely that Stornoway and the castle of Cairn-na-Burgh (surrendered 1504) were both fired upon from the sea; Carin-na-Burgh in particular is isolated a mile from the nearest land. The Michael, built for the Scottish navy beginning in 1506, was designed from the start to carry 12 guns on each side and three bronze basilisks (very heavy cannon).