Just got 2 new rear tires on the C5. Michelin Pilot sport AS ZP. Had the same before. Replaced rears only. Still have good tread on the front.
Now it feels a little like the car is floating. Also on hard braking the rear end does not feel as stable as before. Hard cornering is also a bit flaky.
You might need to give it a few miles on the new rubber. Kinda like heat cycling them. I've always notice new rubber acting that way. Kinda feels like they do stick to the ground.
The tires might still have some mold release compound on them from the factory. As you might imagine, mold release is designed to be anti-stick and have low coefficient of friction.