But France should have cores if she'll be expanding into the HRE, while I believe any HRE territories conquered by the Turks are auto removed from the Empire anyway. Having it apply to everyone isn't a bad idea.
Your points about France make sense. I had a look at the decisions code and I didn't find anything specific for the Turks. They are likely to qualify to remove provinces they capture from the Empire, and a player can easily do so, but the AI may not, as the decision needs a magistrate and the AI doesn't prioritize magistrates. It's certainly possible I'm missing something.
I think your idea is viable, but I don't really like the idea of giving serious penalties for non-HRE countries owning non-core HRE provinces while at the same time making it easy for the player to avoid the penalty by removing those provinces from the HRE. I think a setup where an HRE province gives a non-HRE owner no direct penalty, but it is hard to remove from the HRE, perhaps requiring a core, and it gives the Emperor a casus belli on the country owning it, would work well.