"So far, the two German fighter Geschwader had been fully capables to keep the Axis' air superiority over Northern France and to beat up the RAF"
Poltava I think you're stretching it a bit here - if this was the case why had the Luftwaffe abandoned its bases nearest the enemy it was supreme too? Advancing backwards maybe? Come on mate if you get yourself "2nd Tactical AF Vol 1. 1943" by extremely well respected aviation historian (globally with no bias to either side), you'll read very detailed and extremely heavily researched loss reports for both the RAF and Luftwaffe over N France in 1943. I see no evidence there of the Luftwaffe beating the RAF, rather of an airforce in decline and unable to intercept frequent RAF incursions unless the situation gave them a distinct tactical advantage, or bombers threatened their own bases of operation. Of course they still had successes, but this is not quite the same thing. The truth was that for most of the time the RAF went about its business of dismantling German infrastructure over N France during daylight hours with medium bombers, fighter-bombers and fighters - hardly the sign of the defenders having air supremacy! Of course German unit diaries written at the time might give the impression that they were winning - it's called propoganda!
Regards the P-47; it held no fears for the Luftwaffe daylight fighter force when met in straight fighter v fighter combat, both 1943 variants of the Bf-109G and Fw-190A could handle it with ease when met on equal terms with equal pilot skills (rarer by late 1943), how the P-47's really scored was as escort fighters in situations when the Luftwaffe was targeting the heavies - not the escorts, hence leaving themselves open to counter-attack from top cover whilst concentrating on the B-17's and B-24's, often those Bf-109's and Fw-190's were laden down with extra equipment and unable to defend against the escorts too.
There seems to be a lot of revisionist history going on at the moment and I felt I had to post on this subject to try and put the record straight in a small way. Unfortunately copious posts like this on the internet are slowly but surely disposing of the facts in favour of popular opinion, which is sad especially when you had relatives who actually fought in some of those battles and know the truth, it's kind of changing history to suit personal preferances. Sad really.