We have a french drain along the perimeter of my home. The drain works well, all of the water flows out towards the front yard, away from the house.

But....once the water starts coming in heavy, the drain fills up, water sits in the drain, and absorbs/perocloates into the ground, towards the foundation/basement.

Would it be possible to put a pump at the end of the drain to move water along? If so, what kind of pump?

Tractor Supply has sump pumps. Get one with an 1-1/2" hose flow, not garden hose.

If pump is installed at end of french drain line then you would still be waiting on gravity to allow it to flow to the catch basin for removal. Likely it wouldn't help much on the heavy rain days. A better course of action is to incorporate some surface drainage in that area to shape and contour the dirt and or bullrock so it is kept away from the edge of the home.

A few other tips that may or may not help based on your specifics:
- if gutters are installed on home, they should not dump right at perimeter of home and must not be run within french drain lines. If downspout extensions are taken below grade, run them in parallel with the french drain in a smooth surface PVC without perforations.
- if you need a sump pump in your crawl space or basement, that's your last line of defense. Much better to address the issue away from the edge of the foundation, but sometimes thats not possible with your lot or home.