I do have the marriage cert from Glasgow for 1873. That's how I know he was a widower. That's also how I know their parents' names. However, I have no idea what the 1st wife's name was.
On the marriage cert it has the mother's name as Jane McGuire, but since Francis and Matilda were both illiterate (I know because they both signed with an `x'), they wouldn't have known the spelling of their own names, but rather, simply the name itself. I am making a huge assumption there, but it's because I don't want to discount possibilities, and I am keeping my options wide.
As for location on the marriage cert, all I have is their pre-wedding addresses in Glasgow. I searched the locations in 1871 and I cannot find one of the addresses, while the other appears to be a stopping ground for new Irish immigrants. It had over 150 people at the address in 1871, and 3/4 of them were from Ireland.
I should add that I have also looked for deaths of all the parents, but there are simply too many options. I have Mathilda Burns' death cert in Glasgow, but I cannot find Francis' cert. I don't think it would say anything about Ireland anyway.
Every single family line that I have seemed to go out of their way to hide their origins. I think they were the poorest of the poor and were very distrustful of any authority figure.