What Metternich meant by this line was that France was the most important power in Europe. He was saying that whatever happened in France affected every other country in Europe. He does this via the metaphor of a cold -- by saying that germs that start out in France spread to the rest of Europe.
Metternich said this in the context of the Napoleonic era. During that time, he was undoubtedly correct. Everything that happened in France ended up affecting the rest of Europe because of the power that Napoleon and his army gave France. This power allowed France to spread its ideas and influences across the continent.