Foundation drainage advice

Hello! So I recently found water coming into my unfinished dirt shelf basement during a rainstorm. Called a foundation company thinking that was the issue. Come to find that they say it's more of a grading issue. Called a grading company, and essentially they want to install a drainage pipe along the side of the house that carries water underground out to an emitter. Their plan is to dig 4'' down creating a trench for the corrugated pipe.

Doing a bit of research I assume they are most likely referring to a french drain, and they were very willing to let me do some prep work. I dug down further than their 4 inch recommendation, and around 6'' down I discovered what I believe to be the footing. Doing a bit more internet research I started to see that recommendations for French drains had the top of the pipe at around the top of the footing.

Does this mean that they were about to install a drain much too shallow? Do I need to go deeper? The only thing I can see being a reason for this is the narrow width between the neighbors property and mine, essentially 4 feet from my house to his fence?

At the very least I need the new grade below the bottom of the window sill, as I believe that's actually where most of the water is coming from (between the sill and the window).

Any advice would be so very much appreciated before I move forward with the company or DIY.