International flight with layover – rechecking bags, customs?

I have a flight from Montreal to Newcastle UK, with a layover in Amsterdam. I booked this flight through Delta–the first flight is operated by KLM, second by KLM Cityhopper. Will I need to re-check my bag in Amsterdam, or will I need to go through customs in Amsterdam?

Similarly, my flight back from Newcastle to Montreal has a layover in France–both flights operated by Air France (also booked with Delta). Will I need to re-check my bag or go through customs in France during this layover?

If it adds/means anything, I'm a US citizen with a US passport.