How to level out or grind down concrete basement floor?
I'm surprised no one has mentioned this but based on the statement:


  I had a french drain installed


it seems to me like if you paid someone (assumption here) to install a drain and they left it in a state where it is going to cause a puddle to form before water is able to drain into it, that it should be the company's responsibility at this point.  At the very least, you should be contacting them to get their explanation as to why it was done that way before attempting to undo what they did.