1) the French Fleet was not crippled by typhus in the First year of the war. 2) The Swedish and Russians agreed to send their fleets into the North Sea Drawing off part of the Royal navy's strength and specifically weakening Hawkes fleet. 3) The fluke wind at Quiberon Bay does not shift and drive the French back out into the teeth of the English guns but instead much of the Englsih fleet is wreaked in the storm or runs aground.
Those three things give the French Navy just enough time to sail to LaHeave and Calais and land the troops at Dover.
Yes its a stretch but no more so then the various Sealion scenarios I have seen