Can you marry someone in Falkreath and move into their home? I've wanted to live there for so long

All I know is that you can't buy a house in Falkreath.

Take over Ainsie's cabin to the west of Riverwood. It's not too far from Falkreath.

According to the http://www.uesp.net/wiki/Skyrim:Marriage article on marriage there is no one in Falkreath you can marry.

Or become a thane. Then you can use the jarl's bed. If you don't mind sharing it with him, of course