How about this. It will only work if you have a heck of a lot of money to spare. If invading France for instance from England, have more than one army. Have at least four, with one small unit (say 400 men) separate for each castle the enemy have. Those small units are attached to an army (not literally), and they travel with them into provinces.

You send the armies in different directions, forcing the enemy to spread their armies thinly. Once you defeat an army, you move on to the next province, while leaving the 400 man detachment to besiege the enemy fort. That way, your main army hasn't lost any men to stay behind and besiege, allowing your forces to keep the momentum of the invasion up.

Its a bit of a complicated explanation, so i'll try to shorten it down a bit:

Main Army: 2,000 men (example)
Traveling with that army: 2 detachments of 400 men (as separate armies)

Once the main army defeats the other main army, one of those detachments is left behind to continue the siege, while the other armies head off.