Re: Sending texts from Europe to US :
I have an iPhone with a double e-sim for French phone as well as my normal US phone number.
Am no expert in this area, yet your query deserves some response.
We do not know whether your double e-sim is from a local or international carrier,
or
what the carrier's plan provides for you, or whether you also have wi-fi access.
Apple support's article: Use eSIM while traveling internationally with your iPhone - Apple Support may help
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Re: "Can I send iMessages to friends and family in the US using either my email address or my French phone number, which also allows texts to the US? Is one preferred? My recipients may not recognize my French phone
number and/or they may not be able to accept messages with email addresses".
You can experiment by seeing what sends successfully ... cellular data charges may or may not apply ...
or
If you have wi-fi access: You should at least be able to re-establish contact by e-mailing your phone number to friends and family.
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Re: What is the best thing to do?
If the article hasn't helped: You may want to check with the e-sim provider
All the best :-)
