To use their song, you'd need to get permission or use a different song. If you use it without permission, it's
technically copyright infringement, so the copyright holder can legally tell you to not use their song, but that depends on whether the copyright holder cares to begin with.
So, that's a cold hard fact, I don't think there's any way to dispute that.
The following is just my opinion, I'm not a lawyer, I didn't go to law school, and my only knowledge in this subject comes from a college course I took 3-4 years ago which dealt with how law applies to software and technology, but for the most part, I'm just reading wikipedia.
Fair use is complicated; there are four things that need to be judged, and if one of those things "outweighs" the others, it won't protect you. The biggest problem would be your usage of the entire song in a way that doesn't create something new (i.e., you're just creating "unrelated thing with this song playing in it", which is considered a derivative work, as opposed to parodying the song, reviewing the song, etc). If you were only using a small part of the song in a small part of your game, that's not as balance-upsetting, and you'd have an easier time getting away with it; they'd have to consider other factors like whether this harms or substitutes the market for the song, or whether the inclusion of this song portion is so insignificant that it nullifies the fact that it's a derivative work instead of a transformative work.
Now, as for your title, let's say I wanted to make a train-based game called "The Locomotion". That, by itself, isn't a problem as long as it's not a trademark (and don't worry, trademarks usually aren't granted for really common words or phrases). The problem would be if I wanted to include the song "The Locomotion" by Little Eva; I'd need to get permission first, but only for the song. I could include a song that sounds similar to it, as long as it's plainly a new song. It's not the most kosher thing to do in the world because I'm using the title of a real song while using a ripoff of that song, but it's technically legal.
Finally, freeware doesn't cancel out copyright infringement. Copyright holders
may be less likely to care when money isn't involved and the thing isn't getting wildly popular, but it's
still infringement and they
still have the legal right to tell you to stop using their song. Again, they might not care, but it's still a risk you'd be taking.