Seems pertinent to join with the anti-bourbon forces, considering the possiblity of seizing more Philippine territory. Then again, joining with the bourbons could pose an interesting opportunity for other colonial ventures in the East Indies.
Joining the Dutch would be the obvious conclusion. They can take the Philippines in victory without any great threat in defeat. France simply doesn't have the naval might to threaten Japan.
If Japan sides with France and the French-aligned side wins the Bourbon Wars, could we see territorial acquisition in the Asia-Pacific Region? Say Dutch controlled areas of Indonesia handed over to the French?
And if yes then what might the French call their new colonial holdings?
Think about the possibility of portions of the Spice Trade controlled by Azuchi (or more controlled).
Yeah, that's basically the divided thing here, as frankly siding with whomever will benefit Azuchi in the end.
Siding with Dutch and therefore Anti-Bourbons means being able to attack Spanish Philippines, which is closer to home and allows for easier resources and possibly easier to integrate. Though, the problem I see is if the Habsburgs win and gain Spain, they're going to want the Philippines back. Also, another problem I see with taking expulsing the Spanish from the Manila means a disruption of the Manila-Acapulco Trade
Siding with the French Pro-Bourbons means being to attack the Dutch in the East Indies. Controlling basically means monopolizing the Spice Trade. Another possibility is that this opens more avenues to India.
I kinda see with the Europeans trying to court Japan into the war is that it'll be letting the Genie out of the Bottle, given that Japan will be cracking skulls and taking someone's territory in Asia, no matter what side. Unless they can rope in another Asian power like China or Korea, but that's probably unlikely.
There also another thing to consider: The war in Europe, as IOTL, the Joseph I died in the middle of it, making Charles VI the heir to both Spain and Austria, which didn't go well for the Anti-Bourbon alliance, since they didn't want Charles V 2: Electro Bugaloo.
Given that there are changes to the War such as Brandenburg being Neutral, we'll have to see how that's develop.