Use a French drain when the water has somewhere lower to go. Use a sump pump when it does not.
A French drain moves water by gravity. It suits a soggy yard, a wet strip along the foundation, or a hillside that sheds water toward the house. It uses no power and has no moving parts.
A sump pump lifts water up and out. It is the fix when ground water rises to the level of the basement floor, or when the lot is too flat for a drain to empty by gravity. It needs power, and it needs testing.
Many wet basements need both. A drain along the footing, or under the edge of the basement floor, collects the water and carries it to a sump pit. The pump sends it outside. The table below compares the two.