Well, judging by a few of your past threads, I'd be willing to bet you are going for a "French king elected emperor and centralizes" type thing.
Here's a few ideas I had:
a French king conquers, and pulls a Napoleon (evicting the ruling Germanic dynasties and replacing them with his sons). Eventually this leads to many of the major states (Austria, Bavaria, Saxony, Hesse, etc) ruled by Valois monarchs.
However, the sheer number of Germanic dynasties in the HRE means that probably would not be feasible (anythone else have any input on that bit?), so a possibility I might use for my AAR:
the Frenc reform the Imperial Circle system into something like the stem duchies of old. Each circle is now a hereditary duchy, ruled by a Valois monarch descended from whichever king conquers Germany. Or it could be part of French peerage, granted as an appenage to the younger sons of the new king of France who can't get France itself... either would work.
In any case, the Valois rule the new "Stem duchies," while the Germanic noble houses are autonomous and are represented in the Reichskammergericht (which replaces the Reichstag). Meanwhile the Valois dukes are those in the Reichshofrat, which functions as both the ministers of the empire, and the Supreme Court. Thus you have various Valois members in the states requested, so I think this fits the challenge.
I think you would need long-term French control of Germany, but I don't think that handwaving a French invasion and occupation of Germany is really going to work. The French attempted to do this for centuries and were unable to conquer Germany, not even able to get a border on the Rhine.
I would say that this kind of dynastic domination would have to come from some other POD, something like a Mongol invasion of Europe or Constantinople falling to the Seljuk Turks after Manzikert, a massive POD that could provide for Germany needing outside help in order to survive.
The Valois didn't succeed to the throne until the early 14th century, which is after both those events. So after some kind of disaster, which causes Germany to be suddenly placed on the frontline, the Valois end up appointed to lead one or another of the larger duchies (Saxony, Bavaria or Austria), and through the same multitude of children that they produced OTL end up dominating Germany.
I would say the easiest POD would be to have the Mongols go a bit further, and fight a really bloody battle in Germany. Many of the leading German nobility are killed, but mistakes make by the Mongols mean that though they win, the next battle, fought by forces led by St. Louis (King Louis IX), ends in defeat for the Mongols. Emperor Frederick II's response to the Mongol invasion was to move to Sicily, so the surviving German princes, following Louis' victory, acclaim Louis the Emperor. St. Louis is able to appoint members of his own dynasty (including Valois) to now empty duchal thrones in Germany, beginning the Valois-Capet's domination of German duchies.
Louis taking the German throne signals the effective union of France and Germany. Once in possession of the Imperial throne, combined with French nobles as German dukes, permanently seals the union of the French and German thrones.