We are trying to get Schengen C visa for travel & tourism. Our itinerary does not include Switzerland. However due to availability of slots I would like to book Visa appointment with Switzerland for Schengen C visa.

Will this be a problem?

Basically here's my situation. I am trying to visit France, Italy & Greece. I will stay for substantial durations in all three places. But I will start off with Italy by entering Paris and taking same day flight to Italy. Then go to Greece. From there fly to France and exit europe. French visa appointments are unavailable for two months. What other options do I have? Can I apply with Italy & Greece? They are not my point of entry