Your descriptions are good but still leave some confusion in my mind. Obviously, w/o seeing what you have, I have to envision it. Anyway, maybe what I have to add can help.
You may want to consider building a swale that catches any SURFACE water from rain. The swale should naturally (meaning, using a slight downslope) divert the water to either a catch basin as you suggest but then, once it starts to fill, carry the water to the street. In other words, the catch basin shouldn't fill that much before it starts taking water, say, to the street. Make sure you protect any piping with filter fabric to prevent clogging from dirt and debris. (Use the reference I supplied before.)
You don't necessarily have to do any work right up against the house. Just keep in mind that the more 'surface' area between your swale, french drain, etc., etc., you have, the more water there is to get to the house foundation. Is it an option to have a backhoe come in and get rid of the dirt, then regrade, then put in a stone retention wall? This is a worst-case scenario (but certainly an option.) Did you buy your home recently? Inherit it? Had this problem for years? Just curious because I would think a home inspector would point this out if he was doing his job.
I'm out for the weekend. You can still post up. For now, my best to ya and hope this helps.