I mean, they look vaguely similar, enough that I've seen them confused for each other, and I think they both speak with French accents in English (which is weird, but then again, Lumiere). They could be father and son, if we learn that the butler is around the same age as Théo or Chloé. Most likely Théo. They're both serious and polite.
I mean, it's a little ironic if D'Argencourt's son works for his hated rival.
I can posit ridiculous theories if I want. It doesn't need to have a lot of evidence if there's nothing to contradict it.
Songsilence wrote: I think Jean is much older than Chloe and Theo. My vote is they're brothers. Maybe D'Argencourt even tried to use him as a spy on his rival, but utterly failed. That could be a fun side-story.
Brothers, father/son, whatever works. I do think D'Argencourt is much older, though as his eyes are smaller than the Butler's, whose eyes are wide which is animation shorthand to say he's rather younger. But, Alya is a lot older than her younger sisters, so....