This is a difficult question to answer here. At the time of Beachy head the French had an army supporting the Jacobites in Ireland (in fact the day after the Battle James II was handily defeated at the Boyne and fled back to France) and had no plans for an English invasion. Hell I think the scope of the victory caught everyone, French and allied, off guard. Louis' ministers simply lacked enough time to through together an invasion force to follow up on the victory, much to the Sun King's fury. So what you need is either a POD in early 1690; perhaps the Marquis de Seignelay, France's Secretary of the Navy, prepares a second army for Ireland and once Beachy head happens is able to quickly shift it to invade England instead. Or you need to create a second Beachy head-style victory in 1692, when the French were preparing a full-scale invasion of England on James's behalf: the French losses at Barfleur and La Hogue scuttled the invasion plans.
Not sure which POD would be the best here as both have their positives and negatives, but in my opinion, if you can get James in England with a large army he'd win. By 1692 many of those who supported/defected to William and Mary were thoroughly disenchanted with the "Protestant champions" and had opened negotiations with the Jacobites at Saint-Germaine. Most of the 6,000 or so troops left in England were called-up militiamen, with a core of professional soldiers. This versus a professional French army is going to lose, especially once defections start up. Which is again highly likely. Throughout the Jacobite movement the Jacobites always promised to rise once a French force landed, but the French army never got across the channel. Here we have that army.
Now here's the tricky part; guessing what James II's restored reign looks like. Until the Earl of Middleton came over in 1693, the Court-in-exile was dominated by the noncompounder faction, which was against James making any kind of concession for a restoration, which made sense. Until 1692 the French were dominating militarily and the Jacobites saw no reason to make concessions when it looked like the restoration was inevitable. It wasn't until the failure of the 1692 invasion that, and this is ironic to me, Louis XIV intervened in favor the compounder faction, which was basically the Protestant party of the Jacobites. This was done in order to makes James II seem more moderate and a person the British could rally behind instead of the foreign William and unpopular Mary. So basically a restoration in 1690/92 is likely to see the noncompounder Catholic faction it the ascent, unless Louis intervenes earlier and forces a Breda like declaration. Realistically though, this is my predictions for a James II restoration:
1. Parliament's gonna be neutered. This is the second time in the 17th century that its rebelled against the rightful, divinely ordained sovereign. Charles II was willing to compromise; James isn't.
2. Full-scale freedom of religion for the Catholics and any miniority religion that supported James. The others, like the presbyterians for example, are going to feel the sting of royal retribution. The Anglican Church will be purged of William and Mary's supported, with the non-juring party likely put in charge (the Non-jurors were Anglicans who refused to take the oath of allegiance to William and Mary). Further the non-jurors were mostly High Church, so the Anglican Church is going to remain English and Catholic. Same in Scotland: the Episcopal Church will be reestablished.
3. A standing army, led by Catholic and loyalist Protestant officers. James is going to need it to secure his dynasty and defend his throne.
4. Financial control transferred to the Crown. Not sure if this will mean taxation is now at the discretion of the Sovereign or if perpetual taxes are established but something's gonna have to develop that gives the crown financial independence of any legislature.
5. Full Catholic restoration in Ireland. The Irish were James's most important supporters, so he's going to have to reward them. In that case a repeal of the Cromwellian Settlement, restoration to Catholics of their stolen lands, a return of the Catholic Church and restoration of Catholic civil rights (ie ability to participate in the Dublin Parliament, freedom of worship ex, ex).
6. England leaves the Grand Alliance and makes peace as soon as possible. Its not realistic for England to pull a complete 180 and join the French. England will need time to recover and James will need time to consolidate his return. However, that means the Englishmen serving in the Continental armies are recalled, the Royal Navy is back in home waters and the financial support England gave is cut off. The Nine years' war ends sooner and in a full French victory. Now what that would look like I'll have to research.
Now this is just my predictions, and I don't know if a second Glorious revolution could/would happen, but this is a likely scenario as to what James's second reign looks like.
