looks like a cable housing - replace very inexpensive; it is not repairable.
What is that, a Peugeot? You just need a new cable & housing, like he said. You may as well do the whole bike, cable sets start under $10, if you have some decent cutters you're set.
Yeah it is a Peugeot, my brother found it in a storage unit. I guess I'll just shell out the 10 or so dollars for a new cable. Do I need a specific kind?
The type of housing you need is "shifter" housing. You can get away with using "brake" housing for the shifters, but you might have problems with shifter adjustment. Note that you CANNOT go the other way. Never use shifter housing for brake cables.