This scenario is clearly designed ahistorically, so any and all historical reference you can throw out the window.
Now... with that in mind, would it be safe to assume that the allies would not have the airpower to contend the LW over France? Just like the LW did not contend with the allied air power outside of Germany in late '44 to '45? Because clearly, in this scenario, Germany hold the upper hand much like the allies did in DGS where LW fighters were not allowed to pursue beyond a certain point. So the question is, who is on the offense, who is on defense?
Just pointing at these reasons, as to why not allow allies cross the channel. For the same reasons in the BoB scenarios essentially, and for the same reasons the LW are not allowed to pursue in 44-45 scenarios.
It's up to the staff to decide, it certainly would be a challenge for axis if the allies would pursue to home bases. I would not mind either way. It's just that allies seem to protest as soon as they're not favored, because the allies won the war, they expect to win. Luftwaffe sticks are used to being the underdog, sometimes we win regardless. My advice is, suck it up and have some fun. It's what we do most of the time.
Bottom line is, whatever the staff decide on, it will be fun regardless. Whichever side wins, it will be fun regardless.