I think it would work.

From what I see from this one pic there is no reason for a french drain, especially one near grade and only about 8'ish long. The grade does not slope towards the house, it looks like a slope is beginning on the side and it slopes down in front. But, the gutter downspout is certainly discharging too close to the house. Water will travel horizontally until it finds a way into the basement, so this is probably what is exacerbating your water problem or it may be at the stoop or on the other side as well.

First, make sure your gravel landscape bed is not a sunken bathtub, but higher than grade and sloped away. Then connect a solid Sewer&Drain PVC or poly pipe (leave the corrugated pipes for the farm fields) to the downspout (all downspouts, actually) and run it underground to dump at the front hill. You can buy 4" PVC elbows which will fit the slope somewhat (22.5 or 45) if you are allowed to dump that close to the sidewalk.

Thanks for that input. I forgot to mention that the main problem occurs when rain comes directly the front of the house and bascially contacts the foundation and travels directly downward through the soil. The downspout actually flows into the yard. Here are 2 pictures on the other side of the steps.

The same problem occurs on this wall where the downspout does not discharge into the rock bed. To keep surface water away from the foundation to prevent seepage in the basement, I was thinking of either a french drain or a channel drain placed against the foundation. The rock bed will allow water to easily enter the drain and then I can route it under the ground, and discharge using the popup drain into the driveway. The second and third photos show that the rock bed is at greater elevation than the drive way and where I plan to discharge. Unfortunately, on the other side, I dont have the luxury of the side discharge, so I'll need to trench into the yard and discharge on the hill.

Do you think the channel drains are the best option for removing surface water before it gets to the basement?

Thanks again.

Solid PVC pipes and fittings allow for safe snaking out in case of blockages. I've sometimes used perforated PVC, so the runoff is distributed. The only trouble with that is cosmetic: streaks of very green grass.

I don't think a channel drain will do much if there's no pooling of water. But if there were pooling, fixing the grade would be the solution. Water hitting the siding and running down the wall is not much different than water just entering the open yard - there is not a large concentration of water collecting at a spot.

However, the downspouts are discharging an excessive point load of water only 3' away from your foundation, so run leaders beyond 10' or connect to underground piping to as far away as feasible. Reducing excessive water that quickly raises saturation of the ground near the house is the first solution to accomplish. Hopefully you realize that water seeks level, and the water at your current downspout leaders can flow underground back towards the house.

The second solution is to make sure your grade is sloped down 5% at the house (6" in 10').

I usually don't see french drains contributing much with a grade situation like yours (fairly flat, high field area with perimeter slope if the pictures aren't skewed). But you can certainly install some as a 3rd solution. The deeper, the better. When it comes to french drain performance, there is definitely a best practices to consider. Be aware not all Youtube videos or products at Home Depot meet that level.