Cell Phones

No, the Apps are not stored on the SIM card, they are stored in the phone's memory. But, your contacts list may be on the SIM card. You need to look carefully to see where they are stored, and if necessary move the contacts from the SIM card to the phone memory, before changing SIM cards.

When you get a new SIM card, it comes with a new phone number, which will be a phone number in whichever country you buy the SIM card. If you want people to be able to contact you, you will have to tell them you new phone number, which you will not know until you buy the SIM card. But, once you have the new SIM card, you can text them your new number.

MrsEB, Delete what information, and why?
The poster is presumably going to put her original SIM card back in the phone when she returns home, so she wants everything then to be back to the state it was in.
The question is what will be available on the phone while it has the new SIM card in it, and the answer is that he only thing stored on the SIM card (apart from the info to connect to the service provider) is the contact list, and then it is usually optional whether contacts are saved there or on the phone.

Apps are fine. I'd suggest preloading apps you might use in France (Copilot Europe for navigation, via michelin, air bnb, a bank app for your bank, Paris velib, smart traveler for customs and immigration coming home, uber, next stop Paris, or others you think will help during your trip).

The only worry is that your phone is unlocked and has the capability to work in Europe. I purchased an unlocked phone because the last time it was like pulling teeth to get AT&T to unlock mine. If you say the name of your phone, many here can tell you instantly if it works in Europe - I made sure my phone would work before I purchased it.

The SIM card has your phone number so when you replace it, you will have a new number. Not necessarily a bad thing but something to be aware of.

Apps will be fine.

I suggest getting a SIM card in town and not at the airport. That way if you have a problem you can go back to the shop for help.