Historically various materials have been used for this purpose.
One of the best recommendations I've seen recently is Greenstreak Sheet Drain
Run it from your french drain over the footer and up the new floor. In addition, I have seen a plastic sheet placed over the french drain before pouring the concrete.
A good reference is 'The Original Basement Waterproofing Handbook' by Jack Masters the web site is
You can ask him questions at the site to. Since you have already done it. You probably don't need the book. But you can buy the book at BN.com. I have no affiliation with Jack Masters. I'm just a DIY that has done a lot of research on drainage issues. And I like books!
You probably won't get much feedback from the regulars on this one. They are die-hard external fixes. Which of course is the best way to go and the first thing that should be tried!