From what you've said, it would be a combination of re-doing your landscaping and water-transport to solve your problem.
Hopefully, your drainage problem is not due to your uphill neighbor having 'altered' his landscape such that MORE water comes onto your lot that didn't exist before, or he's altered the lot such that his existing water is entering your property at a place where it didn't enter before, thus, causing you problems. If this is the case, well, in most places, it's illegal to alter the natural flow of water w/o permission from the authorities (and the neighbor(s) it affects). I'll leave it at that. Anyway, I have a couple of suggestions. The french drain needs to be properly built. The builder should line the drain with filter fabric. It should also be lined with concrete block. Also, if the grade is not steep enough, he should be mindful of the frost line. If the piping at any point collects water, it could freeze and eventually block the flow. That's bad news. Also, is he planning on putting in a clean-out just in case it does get clogged with 'stuff'? Have him explain to you how you'd clean out the pipe. And make sure that the entire length of the pipe is accessible for cleaning should it be necessary.
For what it's worth, the expense to do this job professionally is not cheap. In most cases, when the work is done by someone reputable, the high cost translates into 'doing the job right' which is what you want. My neighborhood is a series of homes that are 'tiered' where the neighbor on the left is 3' above me and the neighbor on the right is 3' below me, and so on. Fortunately, everyone gets along and I just went and did the work. The water was natural flow in addition to water off his roof. The roof water coming off his house is allowed to drain on his lot and 'naturally' take its course. I put in a 4' x 2' x 4' drain and ran pipe about 70' to the street. I have 1 clean-out because the run is a straight one. The drain is lined properly and the grade on the left side of the house has been re-done so the water now naturally flows into the drain. It took 2 weekends and cost less than $250 for material. My back did hurt for a while. Good luck!