For yet another possibility to consider (one that, according to this Expressio.fr entry, "est presque toujours employée avec un sens négatif" [is almost always used negatively]), there's:
La caque sent toujours le hareng
(A herring barrel always smells of fish)
The cited entry describes this expression as meaning:
Lorsqu'on a de basses origines, on en conserve toujours la vulgarité,
malgré une éventuelle réussite ...
and proposes two American translations:
"Class will tell" and
"You can take the [person] out of the trailer
park, but you can't take the trailer park out of the [person]" ....
and two British ones (including the expression in question):
"Blood will tell" and
"What's bred in the bone comes out in the
flesh"