It is a very grindy type of scenario, definitely one of my least favorites from the original game. It has that AoE1 feel of an imbalanced, learn by trial-and-error FF that is designed like one of those unforgiving quarter-eating 80s arcade games.
I do believe that the best way to win is to sneak outside the city to the far west and then break in there, near the villagers. Then it's a straight shot to the bridge and the extra gaia units. Most of them are useless, but the scorpions are actually very helpful when that flood of enemy pikemen comes in. When you break out of the city, just split your army in half and have each group distract a wing of the Burgundian force outside of Compiègne while Joan and the villagers run into the city.
Really, the main key is to not go chasing enemy longbowmen all over the map. Ironically for the Franks, the best strategy is not to use your cavalry against them, but instead to keep your force compact and let your crossbowmen and cannons shoot them. The process reminds one of the way the Romans and the Crusader armies (often unsuccessfully) fought roving bands of horse archers in the Levant. You'll want the cavalry to focus down enemy onagers before they hit your army, however.
The towers are really annoying, though. The ES designers weren't kidding when they wrote that line about them into the hints. As you say, the mission got even harder in AoC since the English player is post-imp and benefits from all of the new techs, particularly halberdier and yeomen. I've won the mission several times, but it takes a lot of patience and gamey, exploitative, and unconventional play.