Does the envelope bear a recent postmark? Keep it.

Who sent the ticket? The police or a collection agency?

I got a ticket in Spain a few years ago and tried to pay but couldn’t. I have visited several times since, renting cars each time and have not had any problems. I recently returned from Italy. Whilst I was away a ticket arrived for "circulating in an area reserved for other vehicles" - I am guessing I must have driven in a bus lane. The alleged "offence" was committed in July 2018. Given the timing of the offence, I am pretty sure it was committed after I returned the rental car. So I am not going to pay.

I was a little concerned when I couldn’t check in online for my return flight that an international warrant may have been issued for my arrest . Turns out that Turin airport just lacks the technology for Mobile boarding passes.

I imagine the situation in France is much the same. When it takes that long to issue a ticket it makes it impossible to challenge it and, apparently, also to pay it. In your situation, I would forget about it.

I'd not forget about it. Schengen is an ever developing system, getting caught in it would be messy.
I would check the French website to see if it can be paid and I would use the contact form to send them an email. I would keep a copy of that email in my phone. Effectively an attempt to pay is better than nothing.
I'd also photo the envelope and all details in case you need to discuss details with a border official.

Call or email the French Consulate or Embassy and just ask what you should do.

Plus I think by 2020 or so France and the EU may be requiring Visas of Americans and if you get the Visa no worries.

You don't need a visa. You need an ETIAS, and then from 2021. The same idea (and partly because of) ESTA for visitors to the US.

I wouldn't ignore it. If you really can't pay it save all the proof you have as to when you received it, when you tried to pay it etc in te cloud somewhere, just in case you are questioned about it.
I know the Dutch pursue unpaid fines when you re-enter Schengen, I don't know about the French.

Seriously though, don't forget it. After almost two years living here, I found that French bureaucracy could be a pain. Keep all of the proof of whatever you did, the payment attempt, any messages that you have sent to them, everything will help you in case you get a problem.

The French Embassy will laugh at you, if they even pick up the phone.

Don't ignore it. Make every attempt to pay it and document everything and keep the documentation.

If you get the ticket in Italy, and don't pay it, they usually turn it over to a collection agency in your own country, which makes the cost of paying it much higher.

We received two tickets in Italy a few years ago. We received a mailing from 2 different jurisdictions with no way to make an online payment. I believe we could have written a check (perhaps not a US check) or we could make a bank transfer. We did the latter with all the added costs associated with making a bank transfer.

Stu Dudley