Cat food is a little too rich for dogs. It's upset his system probably. With some good exercise, to work it off, plenty of water to flush it out, and a light (canine-suitable) diet -something like boiled chicken and rice for a couple of days, he SHOULD be fine. But obviously if any symptoms worsen, if there is extreme lethargy or any other cause for worry such as diarrhea, vomiting, or abdominal pain, then take him straight to the vet.
He's probably reacting just as any of us would who have greatly overindulged in food. Cat food, as Ginger said, does tend to be fattier than dog food, but it's not anything that would cause any permanent damage.
Keep an eye on his gums and mucus membranes for the next day or so. They should be a healthy pink color, not a muddy brownish pink color. You also want to watch for him going through the motions of vomiting without producing any vomit. If you see him doing this, put him in the car and head for the nearest vet. If it's during the night, head for the emergency vet. This action could mean that he is bloating, and that because of the large amount of food in it, his stomach has flipped over on itself and has choked off the entrance and exit to the stomach. This condition is life threatening and the dog will die without emergency surgery. Now, the one thing in his favor is that beagles are not considered to be a breed that is prone to the disease called bloat. This usually occurs in deep chested breeds like great danes, collies, greyhounds, and other larger dogs. It's not unheard of for it to happen in smaller breeds, however, so since he has overindulged to badly, just keep a close eye on him.
Chances are very good that all he has done is given himself one heck of a bellyache. I just wanted you to be aware of what COULD happen, however, so you know what to watch for and can act on it immediately if you see any of the signs.
Please post back with any new developments, and please post back tomorrow and let us know how he is doing. The digestive tract of the dog is short and he should be ready to poop out whatever he doesn't use of this food by morning. Good luck and hang in there.
Ghilly