Here are the weapons mentioned in this account, with the number of times mentioned:
Lance or Spear:8
Steel Mallet (martel, mail):4 (a particular weapon is described as weighing 25 lbs.)
Fauchart, fussart, fauchons:2 "with a cutting edge on one side and a hook on the other"
Shields are mentioned four times.
The fauchart sounds a lot like a weapon that's shown both in Queen Mary's Psalter and the Holkham Bible. In the Holkham Bible it is wielded with both hands by the figure on the lower left.
Here is the original French. The dissertation also has a useful who's who of the individuals present.