If Britain had failed to take Louisbourg (or France had managed to retake it in 1746 with the Duc d'Anville expedition), France would have had other options for peace. In 1745 Maria Theresa sued for peace with France, offering to give them parts of Flanders (specifically the districts of Ypres, Furnes, and Beaumont) and give Parma, Piacenza, and Pavia to Don Felipe. This was a pretty good deal, and certainly much better than the deal France eventually got in 1748. But the French refused for two reasons: First, d'Argenson was a colossal fool and insisted that Austria confirm Frederick's conquest of Silesia, which made no sense as retaking Silesia was the whole reason for MT's peace offer to France; and second, that while Austria could fulfill French war aims on the continent, Maria Theresa did not have the power to return Louisbourg, which had fallen to the British earlier that year. If the French had agreed to her terms in 1745, they would have had to evacuate the rest of the Austrian Netherlands, and that occupation was the biggest piece of leverage they had on Britain. It seems very unlikely to me that the British, absent a French occupation of the Austrian Netherlands, would have agreed to return the "Gibraltar of the West" in exchange for Madras. They weren't really equivalent.
If Louisbourg doesn't fall in 1745 and d'Argenson is replaced with someone who was actually competent, it's entirely possible that the Bourbon-Habsburg part of the war ends in 1745, Austria and Prussia fight a 1 vs. 1 duel for Silesia, and Britain is stuck without any continental allies. Perhaps they continue the naval war against the French and Spanish for while, but that war hadn't been going particularly well for them - despite arguably having the upper hand at sea, they had lost Madras and failed disastrously to make any real gains against the Spanish in America. If they fail at Louisbourg and the Austrians drop out of the war, there might be some pressure to cut their losses and make peace. Britain was willing to fight on for decades against Napoleon, but the WAS wasn't the same kind of ideological struggle.