If an amicable and somewhat lenient permanent peace treaty were struck between the Nazis and Petain's government sometime in 1940, could it have brought Britain to the negotiating table as well?
Such a peace would have need to be a threat against Britain. At that time the Brits had already taken Frnce (occupied and Vichy) out of the count, a bit unwillingly in the beginning nourishing their french - at that time just - puppet gouverment : Free France
So, no threat to add, no need to negotiate with Hitler.