Cryptic crossword clue
Influence criminal case due to begin in French city

The most common and most likely answer to this crossword clue is the 10 letter word ASCENDANCY

I've seen this crossword clue in Independent
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Buddy explains!

The straight part
We know that "Influence" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case influence = ascendancy.
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 ASCENDANCY mean?

ASCENDANCY noun
  1. The process or period of one's ascent
  2. Supremacy; dominant control; the quality of being in the ascendant
  3. A class of Protestant landowners and professionals that dominated political and social life in Ireland up to the early 20th century

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