European history's not really my field. That said, some speculations:
If France and Britain have an anti-Hapsburg alliance, presumably at some point they intend to fight some Hapsburgs. Given the geography I can't see a major English land intervention into Germany during the Thirty Year's War, so presumably they intend to operate primarily navally, targeting Spain rather than Austria, and possibly focusing to some extent on colonial gains rather than direct attacks- at least going by the subsequent English history of fighting wars with Spain. So far, so good.
I don't see a high likelihood of France trying to go for the kill and conquer or vassalize Spain. Maybe make efforts to meddle with the succession, or aid Portugal in achieving independence, but total warfare is both out of character for the era and of questionable value to the French, whose ambitions lie primarily in the Low Countries. But a truly successful Anglo-Franco-Hapsburg war would probably make the future history of the Netherlands and Belgium unrecognizable, with the French incentivized to claim territory to their north but probably preferring a Spanish-ruled Holland to an independent protestant one (unless they believe it weak enough to be vassalized), the British incentivized to try to turn the Dutch rebels into a new Protestant state under their influence, and the Dutch having their own interests- and the will and military power to pursue them.
In England domestically, this presumably helps shore up Charles I's position somewhat, especially if there are any successes to boast about. On the other hand, wars are rarely cheap, even with some level of French support- and I very much doubt that the French will invest much in England, when subsidies to Sweden and Denmark to threaten Austria offer a much better per-dollar investment.
Taxation and religion were the two critical factors that drove England to civil war; here taxation will presumably have to increase to pay for the ongoing campaigns and religious strife will increase, if anything, after an alliance with the hated- and very Catholic- French. Does this speed up the outbreak of the ECW? Possibly, but if Charles can spin his actions as a defense of Protestantism in Germany then he might be able to split some of his opponents away from each other. Historically, though, Charles was hardly a master of propaganda and political maneuvering.