Yes, it's possible in French too.
Il y a trois Caroline dans ma classe.
In French, proper nouns never take a plural mark. The noun Caroline in that sentence is plural, but it is invariable. (This may be a mistake that natives make in this case, but I don't think it's raised to the point of being considered acceptable even by most descriptivists.) Similarly, the equivalent of “I visited the Joneses yesterday” in French would be “j'ai rendu visite aux Dupont hier”. “There are 18 Aberdeens in the United States” is “Il y a 18 Aberdeen aux États-Unis”.
There are a few exceptions to this rule. If the proper noun is used to evoke an archetype, then it does take a plural mark, even if it remains spelled with a capital letter: contrast “des Picassos” (some genius painters) with “des Picasso” (some people in a family whose surname is Picasso) or “des Picasso” (some paintings by Picasso). Also, a few historical surnames do take a plural mark (“les Bourbons”, “les Horaces et le Curiaces”). See also Accord du nom de famille.