Bulldogs are also predispositioned to having allergies. It's possible he's having a mild allergic reaction to his food or it could be related to environment (plants he's getting into, grass, pollen, ragweeds).
If it's in combination with eye puffiness, redness, swollen lymph nodes, OR if the discharge changed in color from black/brown to greenish yellow, or goopy instead of dry it's most likely a bacterial or fungal infection that should be treated by a vet.
You could try changing his diet to a sensitive skin formula, one with reduced or no allergens (common dog food allergens are corn, wheat, and chicken). This is a common recommendation (my friend switched his bullie to a limited ingredient diet food that's protein source was fish, and his skin was less flaky and itchy, and the discharge improved).
Also, know a little bit of crusties is normal after prolonged periods of sleep, but I like to never assume, so that my pets health is risked by lack of reaction.