He was sitting in his chair with an absent air about him.
He was sitting in his chair daydreaming.
「彼はぼんやりした様子で椅子に座っている。」を an absent air を使って言うと、例文1のように
He was sitting in his chair with an absent air about him.
と言えます。
with an absent air で「ぼんやりとして」という意味です。
an absent air の他に、daydream を使うことが多いので、daydream を使った言い方は以下のように言えます。
He was sitting in his chair daydreaming.
daydream は「ぼんやりする・空想にふける」という意味です。
ご参考になれば幸いです!