help with researching and paying a traffic violation?

It can take anywhere from several weeks to several months for the traffic citation to arrive by US mail. You just have to wait for it to arrive.

The "bill" from the traffic agency may come a few months after you return home. And the rental company's fee is for providing your info to the traffic agency involved. We got a ticket for speeding (deserved...camera) about 3 months after we returned home. We learned about it first when we got the charge on our credit card from the car rental agency. Don't worry. It will come. We paid the fine online. Pay as soon as you get it because the fine goes up the longer you wait.

Be patient.

You really can not do anything until they contact you, then you will have the information, maybe a website that has pictures or a more detailed explanation, and instructions on how to pay. The most likely method of payment will be through a bank transfer, when you have more info, others on here can give details of what they did.

Also, 3 weeks is a short amount of time in these matters, it may be several months, from Italy, it can take a year until you get details.

As for the infraction, I would be surprised if it were a low emissions zone, maybe a restricted traffic zone, but it could be inadvertently getting in a bus lane, or the most likely is speeding. Speed limits in France are true limits, no "5 or 10 MPH grace buffer". 50 kph in an urban area is 50 kph, not 52 kph.

Edit: It is possible, that once they see you are international, they may also decide to drop the matter, and you see nothing.

I think, but I'm not certain, we drove through a "low emissions" zone
on our way out of Paris.

It's unlikely this is a fine for a low emissions zone. There aren't any between Paris and the Dordogne, nor are there any in the Dordogne. And your rental car is (normally) supposed to have a sticker.

In my opinion, it's more likely a ticket for speeding or parking.

Paul, I'm curious, what do you base this on? Betsy could get false hope.
"Edit: It is possible, that once they see you are international, they may also decide to drop the matter, and you see nothing."

Could you give an example?

We always received them when we lived in the US and rented cars with our US licenses in France.

I'm waiting right now to see if we got tickets. Our son drove us around for our vacation a few weeks ago using the car I own here in France.

The actual ticket will arrive in the mail months later. Ours was 6 months later. The fee from the rental agency is for them to give your info to the police.

Two years have elapsed since I was ticketed outside of Roussillon for going 5 mph over the limit. I've yet to receive anything in the mail. I was afraid that an unpaid ticket would prevent me from renting in France again, but lo and behold I rented again recently and heard nothing about the previous infraction.