I just buy an unlocked cell phone and buy a sim card for each country I go to. When I go to France, costs me 20 Euros for unlimited calls (including to the US), unlimited texts and 3Gb of data.
What if someone wants to call me? If I'm abroad it's mostly for vacation, I can give my new number to family members wishing to contact me.
If I can't do that? I still get texts and voicemails through Google Voice on my phone. And if needed I can enable calls through data on my phone using hangouts.
Another great feature for local SIMs is that they are often "caller pay." So that if your family does want to call your French phone number from the USA, then they end up paying for the call, not you :-)
I'm Canadian, and my first stop when driving into the USA is to stop at the first department store I come across and buy a T-mobile SIM. If they don't have any, I just buy the cheapest "burner" phone and take the SIM out and pop it into my iPhone.
What if someone wants to call me? If I'm abroad it's mostly for vacation, I can give my new number to family members wishing to contact me. If I can't do that? I still get texts and voicemails through Google Voice on my phone. And if needed I can enable calls through data on my phone using hangouts.