The assertion above is not terribly surprising, because England (and then GB) were archenemies of France for so long, both in the original Hundred Years War 1337 to 1453, and the so-called "Second Hundred Years War" (c. 1689 - c. 1815).
So during these eras of arch-rivalry its obvious that a major weakening of England benefits France's relative power position.
However, I would argue that even at many points when they were preoccupied with enemies or in detente with each other, the Britain loses - France wins equation still obtained.
I'll flesh it out with these additional sub-theses:
1) From 1250 on, England was a major power in a good long-run position to develop industrially and to become the # 1 beneficiary among the European countries of trade/exploitation of the non-European world
2) England's odds dipped to their lowest point with the end of the first hundred years war, but then kept steadily rising until the personal union with Scotland was established in the early 1600s.
3) The rise England-Scotland-Ireland (then Great Britain) accelerated ever more rapidly from the the early 1600s, and became ever harder for any European opponent to arrest or reverse through the middle 20th century.
When Britain's relative power position stopped increasing in the 20th century, the principal beneficiary was the United States. European neighbors, with the partial and temporary exception of the USSR, were not in a position to displace Britain's power.
4) What-ifs that derail England's rise are generally more plausible the earlier the divergence takes place. Successful invasions of Britain, plausible at several points from 1250 to the last one in 1688, become ever more implausible with each following century. (ie, Bourbons didn't have good odds of successfully invading England in 18th century, but they had better odds than Napoleon. Napoleon's odds in the 19th century were quite poor, but the Germans odds in the 20th century were even worse, to the point of being the quintessential ASB scenario)
5) Severe weakening of Britain, whether caused by worse internal convulsion or locally focused natural disaster, or by enemy action, would in most plausible cases leave France, and not any other European country, in the best position to take on the role of the mightiest naval, colonial and trading power.
6) Therefore, Pax Francia is almost the only plausible European replacement for Pax Brittanica. While Britain's island geography and geology was supremely advantageous, as Mahan and others detailed, France was in the next best position, on the far western side of Europe.
Applying this to various what-ifs:
If the Spanish Armada succeeded in invading Britain, even if the Spanish succeeded in inflicting maximum damage, Spain's ascendance would probably be ephemeral, with France sooner or later getting more powerful than Spain.
If the Dutch had fought and ravaged England and its navy thoroughly, (instead of moving William of Orange's base of operations there), Dutch supremacy would have been indefensible against France in the long-run.
Any France that succeeded in halting and reversing Britain's rise would have been more than able to hold down the formation of any Spanish, Dutch, German, Italian or Russian bids for the lead role in Europe.
This also means that for any Pax Hispania, Pax Germania, Pax Italia or Pax Russia to occur, they would not only need to defeat England/Britain or have it collapse, they would need to roll 6s again and have France have equally bad luck in order to forestall a Pax Francia.
Thoughts?