I haven't heard of a wallet.wallet file before. Could it be a Multibit file?
"wallet.wallet" does indeed sound like it might be a MultiBit file... possibly MultiBit Classic.
OP, do you remember if your original wallet application looked something like this:
If it did, recovering the funds will require a little bit of work, as MultiBit is no longer developed or supported. As such, you wouldn't be able to send your coins directly from MultiBit... however, you should still be able to install it, start it up, open your "wallet.wallet" file and then export your private keys. You could then then import those private keys into another wallet like Electrum.
From there you would be able to spend the coins and send them to an exchange etc.