OK, chances are you're right - no one will look at either the stamps in your passport or your carte de séjour (which really doesn't entitle you to much of anything, other than stray visits to other Schengen countries while you are resident in France).

I can't advise you to overstay your visitor's visa in Portugal - but I can also tell you that I had no problems studying in France while totally illegally living there. It's working that they are really concerned about.

If the Germans have gotten quite as strict about visa issuance as you say, perhaps you would want to drop the studies in Portugal from your resumé when applying for a visa for Germany. If the program lasts longer than 3 months, it's a dead giveaway you did something wrong that you can't say you had a student visa for Portugal.
Cheers,
Bev