According to French wikipedia, automatic pedals seem to be clipless pedals.
A wide range of manufacturers make waterproof shoe covers (also known as overshoes or booties), for use with both clipless pedal systems as well as your usual set of sneakers (be sure to check out the particular model to see if they're compatible. One designed solely for clipless pedals may be too small for your regular shoes unless you just wear Chucks. Ones which can be used for regular shoes are often marked to work with mountain bike shoes and leisure shoes). They just go over your shoes, and look something like this (not endorsing this particular model necessarily):
But a lot of people commute with their galoshes on regular old platform pedals for a very long time, so maybe you just need a better pair of galoshes?
A big part of not getting your feet soaked is avoiding water getting to them in the first place, which you typically do by using fenders.
Full fenders with mud guards - a lot of water gets kicked up by your wheels, and this prevents a lot of it getting to your feet in the first place. They also help dirt from the road not get into your drivetrain in the first place which is a nice touch.
If you're commuting on a race bike or full suspension mountain bike something, you may not have the brake clearance or mounting points to run something like these fenders (they're some set made by Planet Bike, but a lot of manufacturers make similar ones). In this case, you can get something that mounts solely on the down tube on and on the seatpost:
which will go a long way to keeping you dry (but not as much as full fenders).