Your husband will be spoilt for choice of classy-looking and excellent quality leather bags in Florence.
You could try the San Lorenzo market (next to the S. Lorenzo Basilica) or the Loggia del Mercato Nuovo ( " loggia del porcellino" as Florence people call it): both places are pretty central and easy to find with lots of choices and the average quality standard of goods on sale is really high. In addition, all around Central Florence there are lots of leather goods retailers.
Of course, if your husband is after a branded bag by one of the big international names, Via De' Tornabuoni hosts some of the world's most famous brand names.
Wherever you go, buy from a proper, permanent shop or market stall. I would advise you not to buy anything displayed on a blanket at the side of a street: these goods are often fake and you may incur into fines if the police see you buying one.
I hope your husband finds what he is looking for.
Have a nice time in Florence.
Thank you Elena for your post - I agree with everything she has recommended! The quality of the goods at the outdoor stalls is good, but make sure you look around before buying as there is a lot of choice.
Make sure to not buy from the street vendors with wares on the ground, they are fake and if you're caught buying, the penalty fines are high so better to not do it.