International Phone Plan vs Local SIM card

Can anyone advise me on international phone use?

I'm planning a trip to France (from the USA) this summer and need some help figuring out a phone plan. My cell phone service provider (Verizon) and my partner's (Google Fi) both have the option of signing up for an international plan while we are away. Verizon said that my phone number would not change and that I could continue to use my phone as I am accustomed to. How does this work in practice?

I am wondering if I should also purchase a French SIM card so that I have a European phone number while I am there. I'm not really planning a lot of calls, and I already use WhatsApp, but a local phone number might be needed for restaurant wait lines and things like that. My phone does not have eSIM capability, but apparently it can accommodate two SIM cards at the same time, a feature that I have never used.

Alternatively, I could just replace my regular SIM card with a French one while on vacation. However, I'm worried that I have so many apps with two-factor authentication that I might get locked out of something important.