Millions of people rent cars every year, but if you're not familiar with renting in Europe there are a few things that will smooth the path of your vacation.
In many European capitals and major cities, it is often advantageous not to have a car - parking is difficult to find and expensive, and moving around by car can be slower than public transport at busy times. Unlike the US, many hotels do not have their own parking. So when in Rome, Paris, London, Florence etc. don't rent a car if you intend to just sightsee in the city itself. If you need to get out to visit another town or city, consider taking the train or even a bus. Services in Europe can be fast, frequent and reasonably priced.
When it comes to a larger geographical area like Tuscany or the Dordogne, then you are going to need transport to get about, and a car is the most efficient way to do so. I say this as someone who really likes to take good public transport, and often takes not-so-good public transport. It is possible to get around by bus in areas like Tuscany, but boy is it a logistical challenge and fundamentally you will get to spend far less time enjoying the area. When you have limited time to vacation, spending it on a bus is false economy. Buy carbon offset to cover the CO2 emissions of the car (and your plane ride, while you are at it) if you feel bad about that aspect.
In a previous posting, we'd discovered that American Express Card rental car insurance covered a lot less than in it has in the past. And we weren't sure if we'd be covered for a claim on a "free upgrade" to a Jaguar car in London. The good news is that Amex paid the claim, as they have in the previous 2 instances where our rental was damaged or vandalized. It takes a while -- mostly waiting on the rental car company to provide their documentation of the charges -- but has worked every time so far. The take-away is the same: take the time to read the small print before you go to make sure you're covered.