The most common and most likely answer to this crossword clue is the 4 plus 2 plus 3 plus 5 letter word DIEU ET MON DROIT
I've seen this crossword clue in The Times
D
I
E
U
E
T
M
O
N
D
R
O
I
T
More clues leading to the result DIEU ET MON DROIT
Buddy explains!
The straight part
We know that "French claim on the governance of England?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case french claim on the governance of england? = dieu et mon droit.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.