'The fact that' versus just 'That'
Personally, I like 2 better in writing, although both are possible. In spoken language, I would only use 1. One often hears "the fact that" vilified as being redundant, mostly because Strunk & White say it's never acceptable. It's true that it is often used unnecessarily to inflate a writer's style. However, it's not always inappropriate:
The police confronted him with the fact that he hadn't been where he said he was.
If the "the fact" doesn't add to the sentence, remove it.