changing planes enroute to Paris

You will enter the EU in Paris, Iceland is not an EU-member.

(But you will enter Schengen in Iceland.)

If you want to know where your passport is stamped......Iceland.

EU and Schengen are two different things

And the relevant issue is where you enter Schengen, which is in Iceland. And with your connection, you will be sent through the Iceland entry for your connection, which is passport control. Were you flying, for example, to London from there you would not enter that area of the terminal, no check. Who is in EU or not in the EU has nothing to do with this. You can reference the Schengen Agreement for the explanation.