I had a french drain installed in my basement and the top of its cement sits around 1/8" to 1/4" of an inch higher then the rest of my basement floor. I need to somehow level this out so I can put flooring down. How would you recommend I do this?
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.
From the description, I suggest renting a proper concrete grinder (bottom of the page) from your local rental shop or big box. This will allow finer control and result in a flatter, smoother surface than if you attempted to use abrasive or diamond-bitted handheld power tools.
If you'd rather not go that far, an angle grinder with an appropriate disk would do the job. You may need to skim the resulting surface to prep it for vinyl tile or other flooring sensitive to surface texture.
A big 7" angle grinder with a diamond cup bit would work nicely. You can also get away with the 'masonry grinding' bit sold at big box stores. You should try to get a dust shroud as well, as even a small amount of concrete grinding will send fine dust everywhere.