What about Bonnie Prince Charlie lands in Ireland after fleeing Scotland in 1745. Attempts to regroup against the Hannoverians. Basically what ends up as a temporary situation turns permanent - BPC never getting the French help promised, and untrusting of only the Irish. In the next peace treaty, Ireland is recognized as independent under the Stuarts (the Hannoverians don't like it, but they're a bit busy stamping out Jacobitism in England/Scotland (or maybe Charlie agrees that all "Hannoverian Irish" nobles can be exported to Britain, if London does likewise with the Jacobite-sympathizing nobility. Any way, by the time the dust settles, the Stuarts control Ireland (although they plan to "one day" reclaim England/Scotland, while the Hannoverians control England/Scotland/Wales (and vow to reclaim Ireland, but are secretly glad that that millstone is gone from around their neck)
If BPC marries a French girl it's likely that Ireland ends up emulating French culture. Becoming a French satellite, essentially. To get Ireland actually annexed by France, maybe go with the duke of Northumberland's offer in the 1550s of Ireland to the French in exchange for their support of Lady Jane Grey.