Andy,
Please make sure you downloaded the correct version of JFBConnect for your version of Joomla. There is a separate file for Joomla 1.5 and another for Joomla 1.6/1.7. My guess is that you're using the wrong installer package.
The 1.6/1.7 version uses the install.php file and the 1.5 version uses jfbconnect.install.php file. The right file should only be included in the package you're using (which would be the jfbconnect.install.php file). The install.php (for J1.7 only) should be missing. My guess/hope is that you downloaded both files, but unzipped the wrong one to check for your issue.
Either way, we haven't heard of this issue before, and there are lots of people who have installed JFBConnect on Joomla 1.5 and 1.7, as well as a lot of testing that goes into each release.
If you are still having issues, please let us know what happens when you try to install.. specifically, what error message you receive.
Thanks,
Alex