A book you might want to check out is Miranda Spieler's Empire and Underworld: Captivity in French Guiana. Though the lion's share of the book is about the French penal system established in the colonies in the late 19th century, Spieler has an entire chapter about the state's treatment of convicts in the earlier part of the century that pertains to your question about prisoners in Les Mis.

During the Revolution and after, the state began to introduce forms of civil death and deportation - many of which were ceremonial and theoretical, rather than physical - to separate criminals from the rest of society. This included civic degradation (the ceremonial removal of citizenship, which happened with the émigrés), legal interdiction (the suspension of all civil rights during a prison sentence), civil death (the forfeiture of one’s nationality and loss of all civil rights for life), and systems of surveillance that were meant to control the bodies of everyone outside the legal boundaries of the state. “Prisons” for everyday crimes often weren’t stationary institutions the way we think of them today (though that would change throughout the 19th century). Mobile units of convict workers were a common means of keeping tabs on the bodies of convicts, backed by the conception that convicts were civilly and legally dead in the eyes of the state.

This is one of the reasons Jean Valjean is such a prototypical character for that time period. Around the time that Les Mis takes place, there were an increasing number of territories within France from which ex-convicts were legally barred from living. Spieler provides a map in her book in the chapter entitled “Missing Persons,” if you can obtain a copy of the book. If you get a chance to look at that map, it’s actually stunning the amount of territory that was legally off-limits for ex-convicts to live in (it’s something like 80 percent of the country). Spieler explains one of the driving justifications for a growing police state after the Revolution was a pervasive fear of “the ex-convict”:

The figure who menaced French society of the early nineteenth century more than any other was the ex-convict.  Liberated felons elicited panic and repulsion among officials and members of the public.  From the 1820s forward, ex-convicts became the object of legal and administrative procedures of rising complexity.  Artful police measures arranged for their expulsion from towns and whole departments.  Law acted in conjunction with police power to shape and underclass of hunted and placeless vagabonds (14).

This, of course, is one of the reasons French Guiana developed as a penal colony in the first place: the state had effectively imposed spatial limits on the entirety of metropolitan France such that convicts could not physically remain there. But it also sheds an interesting contextual light on Jean Valjean's continual struggle with Javert and his criminal past, and it shows the extent to which Victor Hugo definitely did his homework when writing the novel.

As to whether or not convicts were used to drydock ships, I can't say, but you have to admit it makes for good symbolic theatre.

It is a form of penal labour which is basically using prisoners as labourers, a practice hundreds of years old and which - in France - only ceased in 1987 when prisoners were no longer forced to work. Penal labour definitely happened in France at the time - save for some brief times during later revolutions - though I can't comment on whether they worked with ships or how many it would take to pull a ship into a dock like that.

An answer about physics rather than history: moving a boat isn't nearly as difficult as one would believe. I regularly move a 100 metric tons river boat by hand alone, without too much effort. It's very slow but not very athletic.

So not only is it realistic, it's not nearly as grueling as one might believe.

I hadn't popped into this thread because I have never seen/read "Les Miserables," but since /u/SerLaron added in a clip of the scene, I think I can comment intelligently on this.

First off, this is clearly something that's being dramatized for, uh, dramatic effect. They're showing a ship with at least one mast trailing in the water and a significant list (lean) being dragged into a dry dock, apparently during a storm, while loose rigging and ropes (and that tricolor) drag in the water. Waves are breaking over the men in the dock (boy, you'd think that ship would keep them out) while they strain to pull the ship towards them (you'd also think that if the wind/waves were blowing into the dock, they'd be running for their lives to get out of the way as the ship is thrown inward). All of this is pretty tremendously implausible; loose rigging would be cut off the ship so it could be sailed back to safety, and no one in his right mind would try to move a ship into a dock when there was a storm going on (what exactly is controlling the stern of the ship and preventing it from slamming into the sides of the drydock?)

I can't really tell what kind of vessel it is from the quick flyover, but it's definitely ship-rigged (that is, it has three masts set with square sails). A ship-of-the-line of the Napoleonic period would draw let's say 20-24 feet of water, and likely more if it was damaged/leaking/listing. (You can compare this to the draft of this model of HMS Victory -- granted, the Victory was/is a very large ship of the line, but there's substantially more that would be underwater than what they're showing there.

Which means that the guys in the bottom of the dry dock would be covered in quite a bit of water -- the ship has to float into it first, of course, and only then can the dock sealed and water be pumped out.

Now, using manpower to move a ship into a dock is not at all unrealistic, but from what I've read, it would be more likely that the ship would be warped into the dock using the standard way of moving ships around not under sail -- which is to say that you'd run a line or lines from the ship to shore and use the standard force multiplier on a ship (the capstan) to apply force and pull the ship forward. You could do that either with a fixed point on the dock, or by say taking an anchor out into a ship's boat, dropping it, and pulling the ship up to it. (Another capstan pic, from the USS Constitution.) It's not at all impossible that convicts could be used for heaving on the capstan, but I can't see what's being depicted in the scene as being realistic and/or efficient.

If I may tack on a question: I understood the scene as the recovery of a warship that was heavily damaged in one of the last naval battles of the Napoleonic Wars, symbolized by the French tricolor being dragged through the water while still attached to the mast. Would that assumption be correct?