The most common and most likely answer to this crossword clue is the 6 plus 5 letter word EIFFEL TOWER
I've seen this crossword clue in The Daily Telegraph
E
I
F
F
E
L
T
O
W
E
R
Buddy explains!
The straight part
We know that "that’s big in Paris" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case that’s big in paris = eiffel tower.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.