Final answer:
At the Battle of Austerlitz on December 2, 1805, the Third Coalition army was decisively defeated by Napoleon's forces, leading the Austrians to seek an armistice and the Russians to retreat.
Step-by-step explanation:
The Third Coalition army faced a significant defeat at the Battle of Austerlitz on December 2, 1805. This battle is often considered one of Napoleon's greatest victories. Facing the Austrians and Russians, Napoleon's forces were highly motivated on the first anniversary of his coronation as Emperor. His tactical genius allowed the French to decisively defeat the larger coalition army.
The Austrians sought an armistice, and the Russians were forced to retreat into Eastern Europe. This victory showcased the prowess of the French military under Napoleon and had significant implications for the political landscape of Europe at the time.