Why were the French peasant so heavily taxed?

That was because Louis XV tried to eliminate the huge amount of debt. When he died, Louis XVI kept these taxes high, because he inherited a more than empty treasury with a debt over 400 million francs. This eventually caused France to go bankrupt.

Also, the French members of the nobility and clergy never had to pay taxes, even though they were the richest. Louis XVI tried to change this, but was criticized so heavily on this idea, that the assembly prohibited him to tax the nobility and clergy.