The comments were reportedly made during Johnson's time as foreign minister, and were cut out of the fly-on-the-wall documentary "Inside the Foreign Office".
Johnson faces Hunt in battle to be British PM
A Whitehall memo seen by the paper said the department asked for the footage to be cut, saying it would make Anglo-French relations "awkward" and make Brexit negotiations more difficult.
Johnson resigned as Foreign Secretary in protest at Theresa May's Brexit plan, and is now the overwhelming favourite to replace her as Conservative Party leader and prime minister.
"The production team made judgments about what was in the programme and they are satisfied that the programme achieves its ambitions and has the content they wanted," a spokeswoman for the BBC told the Mail.
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