During the French Revolution the French National Assembly split into two groups. Those who were more traditional and supported the King sat on the right side of the chamber, those who more radical and supported the revolutionaries sat on the left.

As the assembly continued to meet in the following years, during the Restoration and after, the traditionalists continued to sit on the right and the more radicals continued to sit on the left.

EDIT: I should clarify, they did this to avoid being shouted down by people around them when they stood to speak.

Source:

Leslie Lipson, The Politics of Equality. 1948

hi! If you'd like to read loads on "left" and "right" in politics, dive into this rabbit hole:

• Since when the left/right division in politics exists? - contains a brief discussion, plus a link to a post filled with links on the origin, and later use(s) of the terms "left" and "right" in politics