If Hitler wants peace with Britain, he has to offer Churchill something other than empty words or bits of paper ....
... and even then, something that can't be taken back the instance he (Hitler) decides
So 'Hitler getting out of France' means both French re-armenant plus the basing of British troops in France ... which, given how fast these could march on Berlin, I can't see Hitler ever risking that ...
I agree that the Brits will stick to the peace Treaty, but Hitler will, no doubt, expect the French to get their own back the instance he launches his eastern adventure ....
Of course if Hitler doesn't attack east, things get more complicated ... at some point Nazi death camps wil become public knowledge and there will be an increasing demand that 'something be done' (IMHO the most likley 'something' would be an agreement with Hitler to alow the non-German Jews into the British Mandate of Palestine)