both sides in the war used military observers in hydrogen-filled balloons to watch the enemy's movements

Yes.

Explanation:

Hydrogen-filled balloons were widely used by the militaries during World War I (1914–1918). The main purpose of these hydrogen-filled balloons to detect movements of enemy troops and to provide direction to the artillery fire. Balloons were the targets of opposing aircraft because they knew the purpose of these balloons so they hit it whenever seen by the enemies so we can say that both sides used hydrogen-filled balloons as military observer to watch the enemy's movements.