I don't remember which Orange SIM card it was, sorry. Anyway this was in the spring of 2015 so things may have changed since then. As for Credo telling me I could not use a multi-country SIM card, that was in 2016.
Yes, as Kim says, things have most certainly changed in the last three years. EU "Rome like at Home" policies came into effect last year, and SIM cards like the Orange Holiday SIM will work outside of France now.
At least, is it still the case that a SIM card will change your phone number?
Yes, while you have another SIM card in place, you'll have another phone number. (E.g. a French phone number while you have a French SIM in the phone.). You get your old phone number back when you put your old SIM card back in.
That is the sticking point IMO when it comes to foreign SIM cards. Personally I don't want to be traveling and be unable to tell people ahead of time (before I leave home) what the phone number is where they can reach me.
Well, if you must be reached at random by phone by people who don't have email or can't text you, then yes, you will want to keep your US phone service when you go abroad. But if you have a smart phone and don't need to be reached immediately and directly, there are some tricks to get around this somewhat, if you are willing to spend a little time putting them in place. There are free texting and VOIP (Voice Over IP) apps like WhatsApp and Google Hangouts. Google Hangouts lets you make free calls to US phone numbers, even landlines. I use it even at home in the US sometimes. Google Voice gives you a free US phone number which will work with Hangouts. When I go to Europe, people who call my regular US phone number (which is also my Google number) get through to me instantly in Hangouts (even my bank or anyone with a landline), using whatever SIM card I am using. The phone may have a Dutch phone number, but I don't give that to anyone at home; they don't even have to know I'm traveling.
Google Voice also lets you text for free. But if you don't to mess with this as much, it's much easier just to tell people to email you if they need to talk to you - then call them back in the US wherever you are with Google Hangouts on their landline or cell phone and talk all day if you want, for no cost. (Except Hangouts uses mobile data if you aren't on WiFi.)
Assuming you have a smart phone, I suggest installing Hangouts (and Hangouts Dialer on an Android) anyway. Try it out - you might be surprised how well it works. It's handy to have for various reasons. (No cell service but have WiFi somewhere? Use Hangouts to make a call.)