Son muy suyos
 

Los franceses son muy suyos.
Inglés?

Do you think chauvinistic would be a good term?

It is no the same.

egocentric?

The French are very odd/peculiar.

If the term has a neutral connotation, you may say, the French are their
own people.

This suggests that the French are very peculiar in the sense of strange/weird. While this is undoubtably true :D, I wonder whether ´peculiar´ takes on a less common meaning of 'of one's own', individual, not like others.

The GDO has

suyo1-ya adjetivo ......

ser muy suyo: no le cuenta nada a nadie, es muy suyo he doesn't tell anyone anything, he keeps himself very much to himself; eso es muy suyo he's/she's like that, that's typical of him/her

In American English peculiar generally has a negative context unless it is followed by to. Do you think particular would be a better term?

well , ser muy suyo in Spanish means what Perikles suggested ser muy suyo: no le cuenta nada a nadie, es muy suyo he doesn't tell anyone anything, he keeps himself very much to himself; eso es muy suyo he's/she's like that, that's typical of him/her
but there´s another meaning, for example if the French need Spanish teachers and you go to France, They would hire a teacher from France first, without considering the accent and fluency. I don´t know maybe chauvinistic is the first fit in this context.

Well, it doesn't make sense to me to say "The French are particular" in context, because it means they are fussy. I don't really know how to express "muy suyos" in English when a pejorative is not really intended.

The example of the French is a bad one, because obviously a pejorative meaning is always meant. :D:D