I've driven in France many times and have managed without a GPS in the days before we had them.
However, in my experience, unless you know the area and/or only plan to stick to the Autoroutes it's easy to get lost or get in the wrong lane and find yourself off on a 10km detour, or going around the ring-road for the 5th time looking for your turnoff!
Also you loose the ability to be able to use the D roads and alternative routes which may be more interesting and it makes driving more stressful - especially if you have jet lag to consider.
While you can use a phone/tablet to navigate with Google Maps (or Apps from Navman/TomTom) there is also the issue of the mobile phone signal to consider which often drops out in rural/remote/mountainous areas.
And unlike the dedicated GPS, you are going to be paying for all the mobile data you use when navigating - using your own SIM card from home will rack up huge charges, using a French SIM card is better (you can get them in advance online or at CDG) but if its a PAYG SIM you'll need to keep it topped up and navigating the French mobile network phone systems is fine if you speak French - otherwise go into a mobile phone store, get a voucher and get them to top up for you.
If you have a basic tablet without a SIM card (ie WiFi only) you'll have to "pair" it with the phone to use the mobile network which I know some US phones don't allow - or only use it where WiFi is available (e.g. Hotels).
My suggestion is
- Buy a TomTom or NavMan GPS which includes maps of France.
- Buy the Michelin "Atlas Routier et Touristique" of France to plan your route and look for the green edged Scenic Routes and viewpoints for interesting drives.
- If you are going to be finding accommodations while on the road, then also get the Red Guide Michelin which lists and rates hotels and restaurants and gives you basic information about towns including a local map (I replace the printed maps/books every 3-4 years).
- Get a French SIM card and use your phone/tablet to research your route/next destination when you have a signal.
Hope this helps