It's a nice setup, but that's not much space to garden. You could always look into square foot gardening or other methods to maximize production, though.
As for access, can you get a garden hose in, around, and out? Will a wheelbarrow, rototiller, other garden tools or equipment fit through the gates? (I don't think my tractor and disk would turn around in there). What if you wanted to back up a truck to load or unload produce or soil amendments, bales of straw, bulk shavings...
Gutters and downspouts on the shed to a rain barrel would be a great water-saving touch.
That setup will take some careful management of soil nitrogen (and other nutrients) especially if your hens are on shavings. Alternating the poultry run and garden will help with disease load, but a single year isn't always enough fallow time, so you can't get too complacent.
A setup like this with the coop sitting over part of a catfish (or carp) pond was one design used by agricultural extension in developing countries in southeast Asia and the pacific. Veggies, fish, eggs, and chicken on the table or for sale, and lots of nutrients cycled back into production.