Any work is copyrighted, regardless of if it's specified or not. Your best bet would be decompiling the application to see how it reads the files.

Did you try to find out online about the original authors of the game? For one, asking them about their copyright and permission to remake the game might make your remake way more "legal", as if the game is made with original art and is not made with stolen IP itself, and you get the permission of the original author to use the art, code or name of the original game, you should be quite secure (doesn't mean you cannot be sued as the "original author" might not be the sole owner of the IP, or some other stuff might come up).

More importantly, the original author might have more information about how to get access to the original files, IF he is open to let you remake the game.

If so, the best way is to open it in a hex editor. It will likely contain a table of contents somewhere, so you're looking for something that looks like a list of file names.

A lot of archives don't store the names, just the offsets. These can often still be figured out using a hex editor though, by looking near the start of the file for patterns of data and padding. If these occur with a regular frequency, they often represent entries in a table. Then all you have to do is work out what the data that's being repeated actually represents.

I'd recommend studying a few archives that have already been cracked so that you start to get a feel for the way that archives are usually put together. This works pretty well except for when they encrypt the data, If they do that, you'll need to as conquestor suggests and disassemble the actual game to see how they read the file.