The tricky part is getting them to +200 relations, which is the only thing that will bring them into "vassal" attitude. Keeping them at war for 50 years to avoid independence wars (I seem to believe they can't declare while at war with you, but this may have been changed) really helps maintain things as you did, and meanwhile, park a diplomat in Paris improving relations.
Next try and get rid of your loans, because having these gives France the "A union only in name" modifiers, which can stack to over -100 relations. Unfortunately, you'll also likely be seeing "ignorant monarch" and "backwards monarch" due to Henry the doofus' terrible stats. Just try to ride out the penalties, and when time comes to integrate them, if you can reach +190 from improved relations and any gifts you need, quickly end your current wars, begin the integration, and then declare a new war, with the intention to drag it out as long as possible. My favourite target is Brittany, because it usually has no allies, and is relatively weak, so you can squash them, and sit around at high warscore before the "calls for peace" appear, and only take "concede defeat" as demands, which will help keep your prestige up to avoid the union breaking. After that, cycle to another useless war you can drag out, and then shift back to Brittany, and rinse and repeat.
Again, I may be wrong, and it may actually be possible for PU junior partners to declare independence while at war, but I managed to keep France (and Austria) stable by constantly cycling wars for the first 60 years, and returning to war immediately after beginning the integration (remember that you can integrate while at war, you just can't begin the integration.) The integration tooltip lies, liker so many other ones in this game, and thus yes, integration still occurs while at war.
After a long grueling set of restarts, I finally managed a successful run here, and got super-extra lucky with randomly inheriting a second PU with Austria, only a few years after the HYW.
(EDIT: Apparently the screenshot exceeds my alloted quota. Any advice on fixing this so I can show it? )