We will have a rental car in France and plan to take our own Garmin. Has anyone run into issues with the Garmin car plug not working in a rental car in France? Do I need any type of adapter to make it work?
You shouldn't have any problem using your Garmin as is.
That is one thing the world has standardized on - all cig lighters are the same from Japan to Europe.
Sometimes you might have issues with the plug that doesn't stay in place inside the cigarette lighter. This has nothing to do with European cars, but it has happened to me (maybe the lighter socket was defective). Just use something (like a small cord or something) to stick it in place so that it stays put. In the USA I had the 'luck' of having a rental car where the lighter wasn't working so I had no power. I went to Radio Shack, purchased a charger for the Garmin so that I could charge it during the night and use the battery while driving. Now I carry the same charger with me all the time in case I have the 'luck' of finding a car with no functioning lighter. Also some cars have no lighter, but they have a regular socket. So that RAdio Shack charger would work well too (just carry a EU adapter). Go to Radio Shack and buy one. It's small and easy to carry (the package has several types, just carry the one that works for your Garmin).
Not in France or with the GPS or its plug, but i did have a problem with the lighter/charging connection not working on a rental from a U.S. site. I was 40 miles down the road when my GPS gave out, so I went on just following the road signs. When I returned the car, the agent tested the lighter and found that the fuse was shot. Now, one of the first things I do before heading out with a rental car is test the cigarette lighter.
Many newer cars have another plug, often behind the console. Our Toyota vehicles have alternate plugs in case the cigarette lighter plug is defective or for back seat usage for a variety of devices.