Actually, a typical home would need both the french drain and the sump pump.
The french drain's job is to collect the ground water around the foundation, thus relieving the hydrostatic pressure and keeping that water from making into the basement. The problem is that, french drains are buried deep, by the footing of the foundation and, after they collect the water, they need to be tied to a discharge line to get the water as far away from your foundation as possible.
If you live in a typical home, and not on the top of a hill, you don't want to trust gravity alone to divert all that collected water away from your foundation. You don't want to tie that french drain to the city system waste-water system either, because during heavy rains the system may overflow and back up. You get the picture.
This is why a typical home needs a sump pump tied to the french drain system, to get rid of that water. If you really want to be protected, consider a sump pump system, with a battery-operated backup pump, that will pick up the tab when there is a power outage.
However, you don't need to dig out your whole basement to install a perimeter (french) drain. You can have it installed internally, along the internal perimeter of the basement. Internal french drains have been used successfully for over 20 years.
It is also a good idea to do some work outside. Things like grading the terrain to slope away from the house, and having clean, working gutters with downspouts that extend as far away from the foundation as possible go a long way in preventing basement leaks, making your sump pump work less.