A surviving Protestant Stuart dynasty means there is not going to necessarily be a dearth of eligible princesses because marriages and alliances will change - does Elizabeth and her government still support one side in the Nine Year War and the War of the Spanish Succession etc. There will still be an issue with a catholic marriage though and I suspect there will be an expectation of Charles' wife to convert if she is a Catholic which probably rules out a French or Imperial marriage but not necessarily.
Nine Years' War - I think Elizabeth and her government would still end up siding with the European Coalition against France. Even the very French-friendly Catholic James went to war against Louis and Elizabeth is not Catholic nor does she have the French familial ties her father and uncle had. I imagine she'd also be even more welcoming of Huguenots in England than James was, who would still promote an even more anti-French atmosphere than already existed in England. Having Elizabeth on the throne eliminates the William III-James II aspect of the war which also eliminates the Jacobite risings and the Williamite war in Ireland. It'd be nice to see Monmouth making a name for himself as a commander during the war. The conflict in North America seems likely to go along more or less as OTL. Might it be called King Louis' War by the Americans in TTL? My guess would be that the biggest change to come out of this for England would be that the country involve itself less in the conflict and not emerge financially exhausted the way it did OTL.
Prince Charles is 12 in 1701, which seems the absolutely latest he could be betrothed to a French princess before War of Spanish Succession breaks out at which point I think the engagement would be broken off and that's assuming Queen Elizabeth would be pushing a French match and I'm not really sure why she would be. It seems likely Charles wouldn't marry until after the war is concluded, at which point he's 26. However, Elizabeth, Princess Royal could marry Philip, Duke of Anjou instead of his OTL wife Maria Luisa of Savoy in 1701.
War of Spanish Succession - Based on the outcome of the Nine Years' War, England is in a more advantageous place before war breaks out than in the OTL. I'm less certain about how things might change here exactly but being better off from the events of the previous war, might England continue to fight on longer than 1713? Begin the conflict from a better perspective? Maybe Princess Elizabeth is married to the future King of Spain during the negotiations? The Hanover aspect will probably not come into play since George is quite a bit farther down the succession than he was OTL at this time. More ideas on how this might go down?
If Austria emerges from the conflict much as OTL, I think Archduchess Maria Magdalena is probably still the best option for Prince Charles. If Austria wins the conflict, this is probably an even better match. Prince James could marry Wilhelmine Charlotte of Hesse, Princess Anne and Prince Henry could wed in a double marriage with the Infante António and the Infanta Francisca Josefa of Portugal, which just leaves Princesses Catherine Henrietta and Charlotte unmarried. Unless Princess Catherine Henrietta marries Archduke Charles in 1708 instead of his OTL wife Elisabeth Christine of Brunswick-Wolfenbüttel? Then depending on whichever way the conflict goes, the Queen of Spain is an English princess? Idk, that might be stunning unrealistic.
Thoughts? Advice?