I was searching for an answer of why liberal politics are considered "left-leaning", and Google told me it was due to King Louis XVI sitting in front of his assembly with the conservatives on the right and liberals on the left.
Is this actually where this comes from? And if it is, was it used throughout history to this point or did it just pop up recently? If the latter, why did it reemerge?
Not even close to my field but this is supported by the Oxford English Dictionary:
From the entry on "centre" as referring to those with moderate opinions:
Polit. In the French Chamber (which is arranged in the form of an amphitheatre), the deputies of moderate opinions who occupy the central benches in front of the president, between the extreme parties who sit to the right and left. left centre: the division of this party inclining towards the opinions of the left, and sitting adjacent to them. Also transferred to the political opinions so indicated; and to the politics of other countries. (See also right-centre n. 2.) In Germany the Centre is the Catholic or Ultramontane party. (This use originated in the French National Assembly of 1789, in which the nobles as a body took the position of honour on the President's right, and the Third Estate sat on his left. The significance of these positions, which was at first merely ceremonial, soon became political.)
This is expanded somewhat in the entry on "right" as:
[Originally after French le côté droit the right-hand side (of the Assembly) (1792, with reference to the seating of nobles and high clergy to the right of the Chair, and the third estate and lower-status clergy to the left). The first division of this sort is commonly identified as taking place during the meeting of the French Estates General in 1789. It was then repeated in a vote in the constituent National Assembly on August 28, 1789: see quot. 1837 and the note at centre n.1 16.]
In two of the three entries the earliest such attribution is to Thomas Carlyle's 1837 History of the Revolution in France where the OED cites:
T. Carlyle French Revol. I. vi. ii. 307 There is a Right Side (Coté Droit), a Left Side (Coté Gauche); sitting on M. le President's right hand, or on his left: the Coté Droit conservative; the Coté Gauche destructive.
But was predated by The Annual Register for the year 1829:
"The result of this election proved that..the union—scarcely a natural union—of a fraction of the extreme right or royalist side, with the whole of the left, or liberal side, which, at the general election had driven him from office, was still continued to keep him out."
NB that the OED has entries for usage of the word "right" meaning "orthodox" if not strictly "conservative" from a much earlier date.