Assuming that your Windows partition is mounted as
/mnt and that your Windows username is
hey, first copy the (randomly named) old profile directory to your Ubuntu account:
cp -r /mnt/Users/hey/AppData/Roaming/Mozilla/Firefox/*.default ~/.mozilla/firefox/win7profile
Then quit Firefox and edit the
~/.mozilla/firefox/profiles.ini file, changing
StartWithLastProfile=0 and adding the following to the end:
Restart Firefox. It should then allow you to select which profile you want to use.