Purchased Orange eSim for travel to Norway. My number starts with a plus+??

+33 is the country code for France. So, yes, the +33 needs to be entered in order to call the number Orange gave you.

Need a little bit more info to be sure you get the right guidance....

• did you purchase a voice/data Sim (i.e., has voice minutes and data allowance), or just a data Sim?
• are you planning to use the Orange Sim as primary or secondary Sim (this would make sense if your phone has dual Sim capability and your plan is to keep your US # for making/receiving phone calls)
• +33 is how you start a phone call to France (+ for international and 33 is France country code). Unclear how you got this and how you think it relates to going to Norway.
• did you get Sim cards for all your family's phones or just one of them?

The Sim card defines the phone number your phone has. An Orange voice/data
Sim changes your phone # to a European one (maybe France going by the +33?).
A data only Sim only changes where your phone data comes from, which makes
sense if you don't plan to make or receive calls when out of the US.

If only one phone has the Orange Sim, then if anyone else in the family wants to
call that phone, it's an international call from a US number still. If all of the phones
have Orange Sim's, then you need to program #'s in the phone based on what
country the Sim is programmed for.

Its good to familiarize yourself with the international phone number format. A good explanation is here:

https://blog.talkhome.co.uk/how-to/international-phone-number-format/

I always put all numbers in international format in my phone. That way they always work, regardless of which country I am in, as the phone will do the right thing.