Any way to pay a fee to have my at-home tests become proctored tests?

Don't think so.

AFAIK the only one of those that offers an option for online proctoring (supervision) is the Abbott BinaxNOW test, and when purchasing those, you need to specify at the time when it's ordered if you want the at-home, or proctored version. The packaging is different for the at-home versus proctored versions (so is the price). I'd be very surprised if you could "add on" the online supervision after the fact. It's a mass-market product, I can't imagine they would want the hassle of addressing your use case.

If you want to find out for sure you could try contacting them (good luck with that, it's a giant multinational corporation that's pretty busy). Personally, I'd just leave the tests you have, and use them for their intended purpose (I have about 50 at-home antigen tests sitting around; I'll be taking some along on my next trip for regular self-tests, and nowadays, if I wake up with a sore throat or other minor symptom, I just grab one and test myself). If you need one for return to the USA, just bite the bullet, they're not exactly expensive.

Actually, yes there is. At least for one of the brands, I-Health (White box with orange title) Here is the link for it
https://ihealthlabs.com/products/ihealth-verified-covid-test-service

I think you would have to put each of the brand names in a search engine followed by the phrase telehealth to find out for each brand that you have.

I second Carol. I haven’t tried it but the box (the 4 pack I got mailed for free) tells me I have the option to pay $20 and have it be proctored. I am not looking at it but I think it also says you need to download the app before leaving the U.S., just like the Binax Now.

I was excited to hear about the ihealth tests as I have a few. Unfortunately if you drill down in the FAQ section they indicate that you must have a desktop or laptop. Phones and tablets are not supported.

Another thing to consider: I believe you have to make an appointment for the proctored test with the iHealth kits, whereas with Binax, you can test at any time.

Good information, all. I have both - and will probably put both in my bag next week even though I prefer the in-person testing to come home.

Thanks for the responses. We’re hopeful that we won’t have to test before our return flight on June 14 but we leave from Lyon so in person testing will be readily available. We’ll take some self tests with us in case we get any suspicious symptoms. And being over 65, with departure April 23, we will do our best to get another booster before we leave since that has been approved.