Drainage area for a French drain
This would depend greatly on the slope of the yard on either side of the drain. A (properly sloped) french drain should divert water about 5 times the pipe diameter on either side(assuming slotted corrugated black pipe in sandy soil) which doesn't come anywhere close to the 50-100 feet you need, so you would need a way to feed the drain area. The easiest way would be to slope the surface toward the drain. Plastic sheet buried under the surface, gravel and sand can also help direct water.

But, as already pointed out - french drains need somewhere to let the water out, and also have to be sloped (at least 1/4" per foot) to be at all effective; there are places they don't work and another solution is required.

This is probably a situation where we can provide better suggestions with pictures or diagrams, and a stormwater expert in your area may have even better advice since they're familiar with the soil and conditions in your area.