Cryptic crossword clue
Vigorously approve of crooks kidnapping French drunk 4,11

The most common and most likely answer to this crossword clue is the 16 letter word LIKE GANGBUSTERS

I've seen this crossword clue in The Guardian
L
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G
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Buddy explains!

The straight part
We know that "Vigorously" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case vigorously = like gangbusters.
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.

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