Hi Uvator, welcome to the forums.
Be careful with “If a tank wins a battle in Normandy or Holland, can it blitz an area”. Once a unit has fought in the combat phase, it can no longer move in the noncombat phase (planes are the exception). So no double battles. But let’s assume there’s a tank in Normandy at the beginning of your turn.
Answer to your question comes directly from the rulebook, page 15.
“A tank (or mechanized infantry) that encounters enemy units, including AAA (antiaircraft artillery) units, or an industrial complex, air base, or naval base, in the first territory it enters must stop there and may not blitz.”.
So in your case there would be 3 reasons you cannot blitz through Paris: there is an AAA, there is an industrial complex, and there is an airbase.