majority of things will be closed
There aren't any particular special events in Florence for May 1 - there is a large free concert in Rome but nothing like that is planned in Florence.
Museums will be closed (unless a few declare special openings at the last minute) EXCEPT for Palazzo Vecchio (which will be open from 9am-midnight) and so will many shops even if it is up to the shop owners to decide whether to remain open or close for the day. Unions have declared strikes in the commerce sector for that day if they are made to work.... so it is likely you'll find lots of things closed.
You will find several small restaurants/trattoria and fast food snack places open so you shouldn't have a problem from that point of view.... but definitely expect to spend the day outdoors enjoying Florence from the outside.
If you have the chance and the weather is nice, plan on a picnic and head to Piazzale Michelangelo from which you can enjoy a great view. Explore downtown Florence, from Ponte Vecchio to Piazza della Signoria to Piazza del Duomo. Do visit Palazzo Vecchio, it is a wonderful chance to see the rooms where past and current rulers of Florence continue to preside over the city ;-).