I’ve been reading “Plantagenets” by Dan Snow and on the chapter about King John, he mentioned that before his failed invasion of France in 1213, his commander (William Longespée) stumbled across a French Navy of 1700 ships, and all of the supplies necessary for a major invasion of England. Luckily (for John), the French army were away, and so the English destroyed the ships and the harbour.
It makes me wonder though, would this not have been a crucial and possibly history-altering moment? John was hugely unpopular in England, there was a fresh/near constant uprising in Wales, and Ireland was only recently “pacified”. Many of the barons in England had links with Philip Augustus/Normandy/Anjou already, so would be inclined to pay homage to Philip already if he landed England (if promised lands too) - not to mention how they loathed John. Augustus was also much more impressive a military commander and political man than John (so could secure English barons with usual mixture of bribery and cajoling).
It seems to me, that if this invasion actually happened, it would be very likely that England would be added to the Capetian empire? Possibly 1066 rerun?
Philip's son Louis did in fact invade England two years later, was proclaimed King of England, and one point controlled half the country. After John's death, however, the barons' support for Louis began to wane, since there was no such ill feeling toward his heir, the young Henry III. The battle of Lincoln usually takes pride of place as the great what-if moment, since Louis' loss there (and inability to take Dover castle) forced him to abandon the war.
Basically, you're right that will a little bit of luck conditions were such that the Capetians could have taken the throne of England from John --- but they came much closer to doing so in 1216 than in 1213.