There are a number of programs that will read all the sectors of the drive and try to recover whatever files are found. If you search the forum for "drive recovery," you will see some suggestions.
These programs will usually scan the disk and recover a sample file for free, then require about $100 to unlock to recover the files. Since professional recovery services run in the thousands of dollars, these programs are well worth a try.
Two caveats: Make sure that nothing is allowed to write to the disk, and don't try to format it. This will almost certainly overwrite the data that you need, which is now considered to be free space.
The second caveat: backup frequently.