He probably has a yeast infection. First of all, you should find out if the food you are feeding is causing allergic reaction. Tear draining, especially if it is a lot, will cause yeast and could be numerous causes, including allergies or entropian, or even just the dog food you are feeding. See the "bulldog health" topics about what to feed your bulldog!
Animax/panalog cream with heal it but you would have to get it from your vet. You can also get medicated wipes like Douxo pads, Malecetic wipes, ect. Without a prescription. Once it starts healing you can use witch hazel or generic acne pads (dont use the expensive ones because they have too much medication in them and will bother your dog!) in the wrinkles to keep them dry and yeast free.
I would recommend calling your vet to get animax or panalog cream first, it will take about a week to get rid of the yeast.
Keep the wounds on his face clean with witch hazel until they heal. Yeast is very itchy and that is why he is rubbing his face, more than likely.
I would also check out the allergies article and dog food ratings. Finding out why he is itchy is as important as healing his itch.
I would recommend you take him to the vet so he can look and verify it is yeast.
Everything is trail and error, but calling your vet for advice would be recommended of course. I am not a vet, so my suggestions are based solely on experience with my yeasty Molly girl!

(who is now yeast free by doing these things!)
