So finding Grofaz to be cool ?
First, stick to the historical date, invading France during winter will bring you in real troubles (because of winter and because of nasty events, try it for the fun once before you saved :rofl: )
You need all your troops, don't bother garnisoning USRR frontier and invade Norway later, you need to crush the french army with minimal loses (need the MP for Barbarossa) so you need all your army.
I usualy stick to a working strat : go though belgium with panzers and mot followed by infantry (at least 10 armor divs, yeah I know they are hard to get with the -50 % IC penalty) When you do that, remove most troops along the maginot and put them near Luxembourg and pin down a good part of the french army by attacking it with those troops, it will slow the redeployment of the french army near Lille area (that you want fast) because France will try to defend Luxemboug with the maginot troops. The key here is the classical one, do encirclement, Ghent is a good target, so is Bastogne or Calais, if you destroy 20-30 french divs, you should then finish them more easy. As usual for Germany, speed is the key and HQs are critical.
Your troops needs to be on offensive, it really helps. Use your stukas as much as you can on interdiction mission over important battles. Don't do ground attacks, those are for russians
Even with a perfect plan don't expect to get Vichy before July if you started in April. And remember you need the maginot line (Get Dijon first)
But don't worry, Grofaz is hard (God ! Felling bad to be beaten by AIs !! :rofl: ) and I think HSR gives a second chance to SP with HoI (even with troops pumped from nowhere via events), so it's cool

.
Also, during my buildup, I manage to stop and slow Bismark and Tirpiz construction so they finish near July 40. Then righ after Vichy I can work on the invasion of UK (and don't lose time as winter will come fast and UK is not easy too to get). With UK in your hands, Barb will be a lot easy (or at least a little less difficult) because you don't need to protect french beaches anymore giving you more available troops.
All in all welcome to Grofaz, the place you want to be to get kicked by AI
Edit : Btw HSR is 2.08 now I think.
Second edit : Reread your post, I think you need more infs too, basically you need more infs, more stukas, more armors, more mots

What did you build to miss them ? Or maybe your buildup is not optimized ? Hehe I think I will start a new game now and try to invade US :wacko: :wacko: :wacko: