I will answer with a few points about using Google Maps in Dordogne in offline and also about classic maps. First I should add that I'm a French user of StackExchange, used to navigate with Google Maps or Waze.
Test - Download part
As this offline functionality is quite new on Google Maps, I have to admit that I never tested it before, so I ran a few tests on my own phone (iPhone 5c, you did not said if you were using Android or iOS).
Firstly I tried to download a zone around Dordogne to check the behaviour (how: using this link ): you have to be careful about the size it will take in your phone, as GMaps indicate that the download size may be up to 500Mb, 1Gb or 1,5Gb depending on the zone you define.
But this an estimate value, as before downloading the application said it could be up to 600Mb for my test zone and after download it was only 145Mb. I think I depends on the content, and Dordogne is mainly rural so there are less items.
One more thing: it seems that the data has a limited time validity: tested a few minutes ago, the downloaded map will expire in a month.
Test - Download part illustrations (in French, sorry)
Download screen: here you select the square zone you want to get
Name your selection before download (it's not a search screen, just a pop-up to set a name to the zone you previously selected)
Test - Navigation part
Then I switched off the data communications on my phone to be like you will be when in France. I was then able to zoom in and out in the region I downloaded, keeping a good accuracy (street names, road numbers, even some restaurants and shops were displayed!).
I set a destination point inside the zone and tried to navigate: not working because my start point was outside the zone (I'm in Paris right now). Once I put a start point in the zone, Google Maps was able to provide navigation step-by-step and even an estimated travel time (with "no traffic information" displayed as it is fully offline).
I also used to travel abroad with other map application (not providing navigation) and the positioning on the maps was accurate even without data, so that should not be a problem on google maps.
As a conclusion, I would said that from my opinion it should work. But you should also read the latest part of my answer.
Test - Navigation part illustration (in French, sorry)
Alternative, or additional items
If you are able to read a classic map (that's a shame that many people don't know how to read a map and only rely on their GPS), I would highly suggest that you buy these "good old Michelin map".
For the location you are going to, the number of the map is 329, you can buy it online for example here: http://www.amazon.com/Michelin-FRANCE-Corr%C3%A8ze-Dordogne-Local/dp/2067210467/ref=sr_1_5?ie=UTF8&qid=1451557422&sr=8-5
You can also find them on some stores in France and on many fuel stops, but if you want the English version as shown below, you better buy it before to be sure to find it.
Image of the map:
Those maps are well detailed for travelling between cities (road numbers, distance in kilometers) and detailed, they only miss details of the cities (name of the streets, etc.). And you can also locate on those maps beautiful/interesting roads, highlighted by a green line like in this sample found on the web:
You will also found some points of interests (castles, churches...)