If they come to France still check that the US SIM would work there, or that eSIM is supported. Theoretically it’s compatible but US carriers can be … finicky.
For banking if depositing check can be done simply via the Web, then the app is not needed. Might have to ask your bank. Keeping the old phone would work indeed but not the most convenient.
So… there is what is theoretically possible, what’s pragmatically feasible with your current skillset, what you believe you need and what you actually need.
If you rely on what is theoretically possible and what you believe you need you usually end up with burn out. If you focus on what’s pragmatically feasible with your current skillset and what you actually need instead you WILL disappoint strangers on the Internet but you might remain sane and surely will learn something in the process, thus both improve your skillset AND have a better understanding of what you actually need.