There was. I think it was titled "Moonfall", or maybe "Another Earth". There is also "Oblivion" in which the Moon was partially destroyed. There are probably other ones, too, but I think "Moonfall" is the one to which you are referring. I might just give it a watch in a bit!
But yeah, it would not be a good thing, according to the movie at least.
Try seveneves for an even worse outcome
In "Bruce Almighty" Jim Carrey uses his God powers to move the moon closer to create a more romantic view for his date. If my memory serves correct, the next day we hear briefly on the news about terrible freak flooding over the world.