Trains run every day of the year. On a public holiday, people will be out and looking for a meal, so restaurants will be open and busy.
I can testify from personal experience of phone calls made directly to them asking this very question that several highly recommended restaurants in Florence are either shut completely, or only open for lunch on this upcoming May 1st. I'm sure they will be in the numerical minority though.
I think you're off the mark a bit on this.
Of course there will be trains, but there will be far fewer than there usually are.
Many restaurants and shops will be closed.
There actually are a lot of trains but I would book as soon as possible to avoid high costs.
On public holidays, trains usually run to the Sunday timetable. But, in any case, there will be trains running.
I just had a look on Trenitalia. On 1 May there are at least two trains each hour.Edited: 20 April 2018, 15:16
The problem isn't so much a lack of trains. Those trains will fill up. If you don't mind sitting in the most expensive seats no problem. If the OP doesn't want to risk paying walk up prices for the most expensive seats book now. Now BTW is already late.
Well, currently I can see some trains for €29.90 instead of the full price of €51. But I agree that it is best now to avoid paying a high price or finding that trains are sold out.
Thank you for the advice. I will go ahead and book those tickets.
For those who have made the trip before, were you happy to go midday?