Louis XIV had an absolute monarchy.

Here’s an interesting site that should help explain the differences for you.

http://www.channel4.com/history/microsites/M/monarchy/documents/absolute_limited_monarchy.html

As to Louis VXI – he was forced into accepting this. He was held in Paris and then his crown was “removed” until he signed and swore allegiance to the new French constitution (Sept. 1791). However, the monarchy was abolished a year later. Louis was later tried for treason and executed (Dec.. 1792) So, it’s arguable whether or not Louis really participated in a limited, or constitutional, monarchy at all.