I've twice bought prescription meds in Paris without getting a French Rx and indeed without showing an American one. This may have gone smoother for me because I speak French, but whether you speak the language or not, enlisting the pharmacist's support by confessing that the problem is yours (the magic words are Excusez-moi, mai j'ai un problème) may get you the refill.
The first time it happened, I'd caught a cold in England and was using a steroid nasal inhaler that comes in a brown bottle. I had examined the bottle before leaving home, but I didn't know the trick you have to use to actually see the fluid level. (Simple: hold it up to the light!) When I ran out in Paris, I thought "This is going to be a pain." It wasn't. I went into the first pharmacy I saw, explained the problem to the charming and efficient pharmacist, and gave her the product's American trade and generic names. She looked it up in a reference manual, disappeared into the back of the shop for a moment, and brought out a new bottle. I asked her "Don't I need a prescription?" and she said "Yes, but it doesn't matter."
It cost me €4.00, less than my copay for a prescription back home.
The second time was just last July. My son had forgotten to pack one kind of pills. We had no evidence he actually had a prescription, but the pharmacist was able to sell us his medicine. This was a much more tightly-controlled med than a steroid inhaler, but she was able to help us out. It cost one twentieth of the retail price at an American pharmacy.
I have no idea whether you'd have a similar experience, but it's certainly possible. Good luck!