Sounds like you're using the standard offline installers, and that their file names are not what's expected by the installer.
You could either try to make sure the filenames are acceptable or re-download.
For some strange reasons GOG lately likes putting installers into two files despite them being small enough to fit into a single file installer. Currently HoMM3 is is one of those examples so there should be two files for the installer, one should be ".exe" and one should be ".bin". You could try renaming them "HoMM3.exe" and "HoMM3-1.bin" and see if it will properly install (though don't count on it because sometimes GOG likes requiring them to have specific filenames because of some other stupid/strange reason).
You could also check the filenames when you begin the download and rename the ones you have to match. But it's not a big download so if you're uncertain just re-downloading shouldn't be a problem while making sure you don't rename the downloaded files.
