Two quick solutions. It looks like you have a good overhang above the coop door, and that wind blown rain was not the likely source of your water intrusion, so...
1.) Increase the height of the sill at the base of your coop door. (same principle as sand bagging around your home during a flood - the higher the sill, the higher the water must be before it enters.
2.) Looks like the water is being partially directed by terrain, coming from the run towards the house. A shallow ditch or the like will help direct it towards a different location. this will also reduce static pressure, so you don't find water being forced up thru the ground when you have standing water outside.
So, a couple minutes to a half hour with a shovel, maybe a few minutes with a hammer and a couple nails, and you should have a low maintenance solution for the ages.
/edit you could french drain, too, but as the above poster said, that's a lot of work. I created a bowl to direct water towards inside my run, away from the house, then ditched it to a low point away from run and hen house. Not as attractive, perhaps, but certainly effective.
Outside the run, a combination of berms and ditches built over the last few months helps keep an acre worth of higher elevation property from draining through my run, or staying there afterwards.
A french drain is essentially a deep ditch, filled with a weeping tile (typically nowadays, that's a corrugated plastic pipe with slots in it to allow water to enter, then wrapped in a landscape filter cloth to keep fines out. The pipe is dropped in the ditch, draining to some lower point, usually covered by moderate sized rock, and sometimes then another layer of landscape fabric then a thin layer of sandy soil.
Water passes quickly thru the soil, into the big voids between the rocks, drains into the weeping tile/pipe, and gravity carries it elsewhere. There are variations and disputes about the proper location of landscape fabric, depth of excavation, orientation of the perforations, etc which largely relate to soils involved and rain amounts expected - but this is the general idea...
One option is to just add a LOT more bedding, until the top is nice and dry.
Or, now that the rain stopped, you could try scooping out the wet bedding and replacing it with dry bedding (but more water might run right in, so I don't think I'd try this today.)
Or put in something for them to sit on. Pallets, bales of straw, piles of bricks, whatever you have that you don't mind having wet and poopy.
For a longer term fix, I see several suggestions have already been made.
You could just try to keep the bedding a foot deep all the time, depending on what kind of floor you have. Bedding + chicken poop + water = composting bedding. Great in a garden, fine over a dirt or concrete floor, really bad for a wood floor
Build a floor in there. I see 2x4s just attach planks on the 2x4s. Looks like the floor will be above the water. Also noticed most water near the door. Get some sand bags and place them outside around the coop to keep water out. also gutters may work to divert the water away from the coop.