The speed limits in France are somewhat similar to speed limits in other european countries. They are indicated in kilometers per hour.

Highway : 130 km/h, if raining 110 km/h   (80 mph, 70 mph)
Dual cariageway : 110 km/h, if raining 100 km/h   (70 mph, 60 mph)
Open road : 90 km/h, if raining 80 km/h  (55 mph, 50 mph)
Town : 50 km/h   (30 mph)

(For young drivers or should you tow a trailer, speed limits are different, check below.)

Typical speed limit road sign :

Also, be aware that when entering a town, the reduction of the speed limit from 90 km/h to 50 km/h may not always be indicated by such a road sign, but just by the road sign indicating entry into town. For exemple :
This is the road sign indicating the town or village of Courpière, beyond this sign the speed limit is 50 km/h.
This indicates the end of the town of Champeix, beyond this sign the speed limit is back to 90 km/h (or whatever it was before the town).

Speeding and other traffic offences are subject to on-the-spot fines. Your licence could also be confiscated on the spot depending on how much you oversped.

If your licence is less than two years old, the speed limits are reduced to :
Highway : 110 km/h
Dual cariageway : 100 km/h
Open road : 80 km/h
Town : 50 km/h

If you tow a trailer with combination gross weight over 3.5 tons :
Highway : 110 km/h
Dual cariageway : 100 km/h
Open road : 80 km/h
Town : 50 km/h

1- Driving on the right.
2- Speed limits.
3- Driving licence.
4- Filling up the tank.
5- Highways.
6- Drinking and driving.
7- Driving times and distances.
8- Busy time on the roads.

Enjoy your driving!