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I've run out of space in Reference comments section, so moved here.
You are, of course, absolutely right about youthful fathers, though one should add that girls have become mothers as young as 5 or 6 years old (https://en.wikipedia.org/wiki/List_of_youngest_birth_mothers... However, I'd only accept that explanation if it were usual for birth certificates to mention that a child's parents were adults.
As I see in other parts of the certificate (name + profession, and name + profession, "tous deux majeurs"/name + "tailleur d'habit majeur"), I assume it's indicating that the person is an adult/of [full/legal] age.