Congratulations on your wedding as well as your choice to pick up the guitar!
It's hard to tell if you have enough time to get the song down, as with any instrument guitar takes hours and hours of practice and patience. In the end I suppose only you will be able to decide if you're in good enough shape to play the song at your wedding.
Looking at the video there are some unconventional voicings being used. However he does play the regular C chord in there.
What it means when he says F over G bass is that you play a G chord, but instead of playing G as your lowest note, you play F.
If you're having a hard time figuring this song out from the video you posted the link to, try to listen for the notes that are being played and just try to find them on your guitar that way.
Hope this helps!
Good luck!
Regards, Henrik