If the water entering the basement is only at that one corner then a sump
in that corner will solve the problem.
Everyone recommends drain tile all around the foundation because you never know when a long rainy spell could result in water seeping up in other places in the basement.
If the French drain* outside is below foundation level then it can be tied into the sump (pit) and no additional drain tile is needed. You would need to run a pipe under the foundation footing to connect the French drain with the sump.
* French drains can be either on the surface or underground. Those on the surface do not need to enclose the collected water such as in a perforated pipe.