I'm not at anywhere near the stage of producing something like this, but I was curious as to what the copyright laws are.

So, in the movie Fast and Furious 7, there is a scene at the beginning where the 'team' drops cars from a plane with parachutes that land on a mountain and then chase the bad guys.

Is that an idea that can be copyrighted?

So if I made a game, and then had a mission where you dropped from a plane, the car deploys a parachute and lands and then it plays out like the movie.

Is that protected by the company?

Would someone require permission to create something like that?

It depends on how litigious the film company is. I would say no it isn't and I'd also say there have been other films and TV shows where people parachute out of planes in cars so it isn't even original.
However MKR did attempt to sue Capcom (but lost) over deadrisings similarity to Dawn of the Dead.

I think you can copy it as long as you don't use the same dialogue, as that's a real thing, and just an idea.

No, you cannot copy it in your game, but if you have legal documents than you can do it. By registering, you are putting the public on notice that you are using a certain mark. So if someone is thinking about using a mark similar to yours, and they conduct a due diligence process prior to using the mark, they are likely to find your mark on file at the United States Patent and Trademark Office. For more information, visit this also.

O_o did you read the comments from Tom and Luckless above yours? They pretty much contradict exactly what you are telling the OP here, and to my knowledge are spot on.

Your statement would be correct if, and only if, the OP would take the scene from the movie and reproduce it exactly (maybe even go as far as taking the actors faces for the characters in the scene)... that would be a big no-no without a license from the movie IP owner.

But as Tom has put it above, that doesn't seem to be the OPs question, and it doesn't sound like it to me (and at least 2 other people)...

Also, I don't think parachuting cars out of a plane is original enough to even try to defend such a case (apart from the mentioned exact reproduction of the scene)... many movies did that WAY before the first Fast and the Furious movie was out. Landing on mountains part sounds more original (if slightly too trashy for a non-cartoon, non-trash movie), but I wouldn't bet on this never having been done before.

TL;DR: This scene is only slightly more original than a mexican standoff in a spaghetti western, or a generic car chase scene in an action movie. When so many movies have done it way before, the concept becomes so generic that you will never be able to hold up a case.

Reproducing exact scenes is something different, but this is pretty obvious I guess... the grey area between okay and not-okay is a dangerous one though, so it is better to take the concept and then create your own thing without too much reference to the original.