The French system has a weak point when it goes to collecting fines past the borders, at least for traffic offenses. Even speeding tickets do not follow through when foreigners get back to their home countries, unless arrested by police directly. At least for now, since the government is in the process of partnering with other EU countries to be able to claim speeding fines to foreign drivers. I don't know if parking violations are concerned, as they are relatively small fish.
The aformentioned advice is not here to say it's okay to break driving laws, anyway.
It is the rental agency that you should rather deal with. Once they get the ticket registered with your car, they can forward the fine to your credit card with additional processing fees. Therefore, I would advise you to call them, tell them about the ticket and ask them what to do next.