I mean, sure, he wanted to be King of Duloc, but since he married the Princess of Far Far Away, surely he should be King of both Duloc and Far Far Away. I mean, in Shrek 3, King Harold says,
This kingdom needs a new king. You (Shrek) and Fiona are next in line for the throne.
Now, if he married Fiona and they went to meet Fiona’s parents and if events led to King Harold still being turned into a frog and dying, would Farquaad be King of Duloc and Far Far Away?