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.

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.

I remember that movie and that scene. :)

Try seveneves for an even worse outcome

Counterpoint: in Despicable Me the moon was shrunk and brought down to Earth with almost zero consequences... so maybe it would be just fine!

Haha, indisputable counterpoint! :D

Seveneves by Neal Stephenson was a good book that goes into what happens when things change between the Earth and Moon.