Going to France from US in September. Connecting through Heathrow and aware of all restrictions. Any updates on what the airport situation is like getting in/out? Long transit wait Heathrow between flights so should be ok there but what about arriving and departing France and having to show our proof of vaccination? And, on the way back, our negative test result to get on plane? How crazy is it right now?

What is happening now has no relation to what the situation will be in September. Even which LHR terminals which airlines will be using is in flux. Ask again a week before your trip . . .