Sure.
The problem is that a single lever will send a "close" task to a drawbridge and an "open" task to a floodgate. That means that you have to be creative if you want to make this thing work.
One option is to run a trigger (either to the floodgates or the bridge) through a water-logic NOT gate. That's sounds complicated, but it's not so bad. Basically, you have to make a second trigger area, such that the lever triggers a hatch, which, when open, drops water onto a pressure plate set to only trigger when there's no water on it. You need a way to drain that water too, so its resettable; you can do that via a powered screw pump, activated by a pretoggled gear, that drains water back to the top of your not gate, or you can attach the system to sourced water, and drain it from the floodgate via, for instance, a raising bridge connected to the map edge.
If that's hard to wrap your head around, that's understandable; it takes a lot of fiddling with levers to start to be able to understand DF water logic, but the wiki page linked to will explain if you're willing to study and experiment.
The diagram I posted showed an alternate path for your bridge entrance. Right now, you have it such that when the bridge receives a "close" trigger, it blocks access to your fort, but with a little redesign, you can make it so that an open (lowered) bridge actually blocks access to your fort, and a closed bridge allows access to your fort. That way, when the lever sends a "close" to your bridge, it opens access via that route at the same time it sends an "open" to your floodgates.
I suppose both of these might be too complicated, when the really simple answer is, "Don't use floodgates for your rear entrances. Use two more small bridges instead." That would solve your problem just as well. It's just that simple solutions aren't very interesting, when it's the perfect opportunity to become familiar with more creative solutions.