#IfWinActive [Chrome's window ID, I'll explain later]
MyClip := ClipboardAll
Run P:\ath\to\firefox.exe %Clipboard%
Clipboard := MyClip
That's an Autohotkey script, which would mean you had to install autohotkey, but if you don't want to do that, I can convert it into a standalone .exe.
In either case, the two things that need to be changed are the P:\ath to firefox, and Chrome's ID. I don't have chrome installed, but the Window Spy that comes with AHK can get the ID of a window, so that would do. Then, once you'd stuck this script in a text file with the extension.ahk and run it, would have Alt-F as a "firefox" key, which would quickly copy the current tab URL in GChrome, open that in FF, and return your clipboard to it's old self. AHK is very light (My 1000-liner is taking 10mb of RAM right now (To be fair, it IS running a few extra clipboards, so I don't know how much of that RAM is that), but my 15 line "Gaming Essentials" takes up something in the few kbs), so won't impact performance at all. You could also do a GChrome button, to take FF back to GChrome, but I don't know if chrome accepts the same command line arguments. If you need any help setting it up, I'm always happy to help :)