It isn't at all strange for that time period. For over a century prior, and still at that period, and far later as well, French planters (both white and mixed-race) sent their children (both legitimate and illegitimate) to Paris to be educated as free men, and many, particularly illegitimate children who were technically slaves in the sugar islands, stayed because this was a very easy way to emancipate favoured bastards. Moreover, many families who owned lands in the colonies acted as absentee landlords, so one could very easily send a favoured bastard to be educated in France, he would be emancipated by default, and be able to inherit and run the lands from the metropole rather than coming back to a deeply and very complicatedly racist culture in the islands. In mainland France, race was not a significant factor and generally came up as a physical descriptor or a way to severely insult someone you hated for other reasons. Alex Dumas was an outlier not in his race but in his military career, and even that was a factor of the times in which he came to France. His son, Alexandre Dumas père, was not an outlier in the least.
Enjolras, or any of the students - even Marius - are the most obvious characters who could have been black in that period, largely because you don't even have to consider whether you want family members to "match" when casting. Valjean, not so much only because of the way the plot functions, and same with Fantine, because of Cosette - with Valjean and Cosette on the run, they'll stand out less. Thenardier family, Javert - could work. Would probably have come from a port city originally, have been sailors or descended from sailors, or from servants brought home to the metropole by landholding families. These are the major inroads for working-class black population in this period.
But considering all the other ways in which the musical makes it a little difficult to believe that Valjean can't be easily found out (brand or numbers on his chest? Numbers, especially, wth, original lyrics?), it doesn't matter if Valjean is white, black, or Iranian. Race never comes up in the source material (the novel has one black character, and he's just part of the list of Patron Minette members), so race has nothing to do with the show and can be ignored in the casting.
What kind of literature and what kind of life is the same question. - Tom Stoppard