Get on with strike over object, maybe, of French leader? (3,2,3)

I believe the answer is:

hit it off

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'get on with' is the definition.
(thesaurus)

I can't explain the rest of the clue.

(Other definitions for hit it off that I've seen before include "Be well suited" , "Develop a good friendly relationship" , "Click with someone" , "Become compatible and friendly" , "Agree - get on well together" .)

I've seen this clue in The Irish Times.

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