British victory and Mahan's appeal to Congress

Is Mahan saying that the British system defeated the French system?

Yes. That interpretation also supported his case for naval construction before Congress, helping explain its emphatic language.

British victory is understood here as the success of a strategic system. Mahan was also trying to persuade Congress to build a navy, which gave his language an advocacy purpose. His claim that England was saved at Trafalgar receives some rhetorical latitude. Napoleon's invasion plans were already failing before the battle.