What type of clothes does the Franklin wear in The Canterbury Tales?
Chaucer doesn't actually specify what sort of clothes the Franklin is wearing. The General Prologue entry for him details mainly his natural diet, which changes with the seasons, and specifies that
An anlaas and a gipser al of silk
Heenge at his girdel, whit as morne milk.
An "anlaas" is a a dagger, and a "gipser" a purse: and the two hang at his girdle (which was) as white as morning milk. That's all we get!
The only other option would be to have a look at the illustration from the Ellesmere manuscript which accompanies the Franklin's Tale. However, there is no guarantee that the illustration was ever seen by Chaucer, so you shouldn't take it as a definitive version of the Franklin!