Complex sentence: Thiers had spotted the first rise of French enthusiasm for the First Empire that would go on to become the Napoleonic myth and thought that returning the remains would seal the accords between France and the United Kingdom even while the Egyptian affair was beginning to agitate Europe.
Split into simpler sentences: Thiers had spotted the rise of the French infatuation with the First Empire that would go on to become the Napoleonic myth. He also thought that returning the remains would seal the new spirit of accord between France and the United Kingdom, even while the Egyptian affair was beginning to agitate Europe.