Just learned that this is a public holiday. We will be in Paris that day so now I'm wondering what to expect in terms of store closures, transport schedules, etc.

It is a non event for tourists unless you need to go to a bank or a post office (or take your children to school and go to work in an office, which is highly unlikely).

exactly, it'[s not one of the biggest holidays. Transport schedules are always different on Sundays and holidays, you can look them up if you are worried about it for some reason. I never give it a thought, there are some longer times between trains/buses, doesn't matter to me that much. IF you don't worry about Sunday, don't worry about holidays. Some transport schedules are different on Saturday, also, which is of course logical as most people work during the week, so wouldn't be cost effective to have the same schedules every day nor every hour of the day.

Thanks! It shouldn't affect our plans at all.

It may be busy; many people in Europe take a 4-day holiday, it's a popular time for city trips.
Nothing you can do about that now, though!