Data carving (with something such as Foremost) works outside the file system, looking just at the data storage directly, so in some ways it is not affected by the file system. But of course it does somewhat depend on how the file system stores the data. Most common file systems commonly store data in contiguous areas and that is why file carving works and can recover whole files. It is possible for some unknown file system to scatter small data chunks all around I suppose, making it much more difficult to detect files and really really difficult to put together whole files. It's also possible for the data to be encrypted or encoded somehow by it.
Photorec works well recovering files from raw data (disregarding any file system) for many different file types based on identifiers for each file type supported). It's free and open source. There are also other good non-open source tools for that such as R-studio and ReclaiMe.
What file types are you going for? Some are easier to carve than others. Some you may even have to carve completely manually. As I said it's also possible the data is encrypted or encoded somehow if you're not finding anything with common file types. Have you looked at some of it in a hex editor? Winhex is a good one for Windows. That might be a good next step to get an idea of what is there. Otherwise you might be spinning your wheels.