The credits are given BEFORE the act as the programme goes along.
The band's name is MARFUL, and they are Galician (NW Spain)not Corsican, so I guess the language is Gallego (the Galician language). The style is a bit like Portuguese fado (Portugal of course being a near neighbour of Galicia.)
The lady's name is Ugia Pedreira.
More about them here:http://www.rootsworld.com/reviews/marful07.shtml
and here: http://www.bbc.co.uk/scotland/music/celticconnections/2010/artists/marful/
And they have their own website, and there are quite a few Youtibes of them.
"Horo Gheallaidh" is one of the best music programmes on TV, but sadly (and this is a bone of contention!) not yet availble on Freeview, only on Freesat or Sky - BUT as has been pointed out, it can be watched by UK residents at least with internet access via BBC iPlayer