Your PX10 deserves better than what you're giving it. That's not a Competition V4 nor a P3 headset. It doesn't even look like the headset parts are all from the same headset. If you bought that headset used and someone claimed it was Stronglight, "for a PX-10", "P3" or "V4" you need to return it ASAP, you got robbed. It's possible whatever you're using isn't the correct stack height either.

The crown race shown looks to be pitted to hell. You shouldn't be using captive bearings on the lower race, use loose bearings. If you overtighten or install the captive bearings upside-down, things will feel notchy or rough, the goal is to tighten enough so there's no play after fully tightening down the top nut, but it also doesn't feel indexed (notchy). I'm not sure if you can get there based on what I'm seeing.

If it helps, on the P3/V4/S5 headsets, Stronglight typically stamped their name into the edge of everything except the adjustable cup: On the edge of the crown race, and on the part of the cups that inserts into the head tube (see below). The P3 and V4 had differences, with the V4 having V-shaped bearing races (buttery smooth!) and the outer edge of the top on the V4 cup having a sharp angle almost like the one you posted above (see bottom cup in pic below).

That said, I would start with a proper, complete French headset in this case, something with something correct for the bike. I can donate a mostly-complete P3 headset (lacks the top nut and crown race) if another BF'er can commit to helping get you a P3 top nut and crown race for no more than the cost of shipping.