。
My father took his seat at the table.
Literal
Father [topic-は] table's own seat [at-に] sat-down.
自分の席に着く simply means 'to take one's own seat' — 着く ('to arrive/settle into') paired with 席 ('seat') is the standard verb collocation for sitting down at a designated place. No 上座 (seat of honor) is specified, so the formality is neutral.