The Battle wasn't sent to France to attack bridges or provide CAS. It was sent there to shorten the range to Germanys industry. In hindsight I wouldn't have built a single Battle I would have built more Hurricanes and put a couple of cannons and a bomb under the additional production to strafe and bomb the bridges in question. However in hindsight I would have just blown the bridges up when the French had control of them.
Very good points. In defence of the French (and Belgians), a lot (perhaps even a majority) of the bridges RAF and French airmen died trying to take out were German pontoon bridges.