Definitely very tough for the Luftwaffe while the French are still around.
Yes, how to defend against strategic bombing in the early game is a puzzle.
I tried having fighters on active, that was a disaster as they get overwhelmed by the more numerous allies - it cost a lot of production and risks them losing experience if they get heavily trashed.
Maybe you could keep the medium bombers at bay by bombing them all out. The problem with this is it ties up the Luftwaffe and is probably not going to be 100% successful. The heavy bomber can stay out of range. However that ties up the Luftwaffe, the priority at this stage of the game has got to be to take out France ASAP.
Haven't tried AA, maybe it would help. That is a lot of production tied up in the early game when the Germans need to be building more units for Russia.
Once the Allies get past the border production sites then Axis can use fighters again for defence, but anything that is within range of the Allied fighters is a problem.
What I am wondering about is how things are going to pan out down the line. Am guessing that I will be able to protect Germany OK after France has gone and the Luftwaffe will be able to withstand the RAF. But what happens once the USSR is invaded, Axis can hardly afford to leave a stack of fighters behind unless they build more - but the UK can build up their bombing/escort force too.