Nathalie from France asked me this question so I'm going to attempt to answer it. This is just my opinion - not an official stand or statement of The Church of Jesus Christ of Latter-day Saints.
"We claim the privilege of worshiping almighty God according to the dictates of our own conscience and allow all men the same privilege. Let them worship, how, where or what they may." [Articles of Faith, Joseph Smith]
We all have our free agency to worship and marry whoever we wish. An atheist can marry a member of The Church of Jesus Christ of Latter-day Saints. My main question is why would they want to?
Our lives as members of The Church of Jesus Christ of Latter-day Saints are centered around God. What would an atheist have in common with someone that worships God and his son, Jesus Christ? We aren't forced to spend time going to church and participate in church activities. We don't have to do anything at all but we desire to.
Because of the knowledge of the plan of life, we desire and want to spend our time sharing our knowledge of what we know to be true. It is a natural expression of our love for God to want to learn more about Him by attending Church, studying His Word, keeping His commandments, doing what he would want us to do and trying to become more like Him.
I know a member of The Church of Jesus Christ of Latter-day Saints wouldn't be happy being married to an atheist so I'm assuming the opposite would also be true too. How can someone be convinced or prove that there isn't a God?