What class did King Louis XVI want to raise taxes on?

He tried to - in order to deal with the crippling debts of the French state (mostly incurred by various wars - most recently the French help to the American War of Independence), but he decided that he did not have the authority to impose new taxes. He turned first to an assembly of nobles (it is not true that French nobles paid no taxes - but they were free of some of the more important taxes) and then called an “Estates General” (the first for more than a century) in the hopes that the nobles and church would agree to contribute more money. But the whole thing got horribly out of hand (partly because Louis XVI was a very weak man - but also because he went into mourning for a dead son at a key time politically) and the French Revolution was the result.