The most common and most likely answer to this crossword clue is the 7 letter word EMIGRES
I've seen this crossword clue in The Guardian
E
M
I
G
R
E
S
Buddy explains!
The straight part
We know that "French aristos unable to adapt to new regimes" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case french aristos unable to adapt to new regimes = emigres.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does EMIGRES mean?
EMIGRES noun- One who has departed their native land, often as a refugee.
- An emigrant, one who departs their native land to become an immigrant in another.