Look at the composition of the French for the answer:
The cavalry portion that was engaged could not have been more than 2500. It was not 6500 cavalry engaged. That is the key to understanding this engagement.
The other is poor deployment by the French. They put the infantry on the flanks with cavalry and guns in the center. This allowed the cossacks to outflank them.
The engagement actually was more like 4000 Allied cavalry vs. 2500-3000 French cavalry. The infantry played only a small role in it.
I am going by the text of Nafziger for this. He does not ref. his source for the captured dispatch but it says that they had 4,400 cavalry and 600 infantry. The Austrians may have been approaching ... he never ref. them and you may be correct that they were never engaged. Why he would mention them in his text if they were not there would be a mystery.
But at any rate I feel that the poor deployment of infantry on the corners with cavalry in the center has much to do with it. Not all of the cavalry was deployed here either as more cavalry arrives as the action is underway.