No, that’s really not OK!
And if that “pop up” is so big that you noticed without being told to look for it, I’d say the saddle really doesn’t fit.
Usually, this means the saddle is too wide in front and/or it fits ok further back under the stirrup bars but opens up to a set of shoulders/withers that are wider than what your horse has. And also (and more often) it means the tree is too “banana shaped” front to back.
Also, IME, the Frenchies really can’t do a wide tree very well. That’s because (I hypothesize) the banana-shaped tree plus foam panels always invite the gullet of the saddle to be too wide at the top. The British, who start with flatter tree, have better luck with building for wide horses.
In any case, to check out the “too wide up top” hypothesis, put the saddle on the horse naked. Slide it back until the saddle stops. That’s where this saddle will sit on this horse, just about no matter what you do with pads or breastplates or superglue. Evaluate its fit from there. Now look at the leading edge of the panel by the withers. A saddle that “opens up too wide at the front” will often have panels that do nicely parallel the horse’s back further down. But up by the top, near the gullet, the saddle comes off the horse. There’s all kinds of room up there.
To look at the curve of tree, look at how much the panels rise up off the back before the cantle. Some rise is OK and part of the saddler’s design. But if you can roll the saddle back and forth on your horse naked, it’s a just about a deal-breaker in my world.
The big deal about a saddle that rolls front to back like this is that it has a rolling-pin like effect on the long, thing pair of muscles that run along the spinal processes. IME, you can make a horse quite sore quite quickly by using a rolling-pin close contact saddle on him! Be careful with this particular fitting problem.
And in general, the more educated you can get about saddle fit and feeling your horse’s back and muscles for what’s normal vs. not, the easier (and cheaper) time you’ll have saddle shopping. It really isn’t rocket science. But you, like the fitters, have to put in some time to learn what’s good fit, ok fit and “it will hurt him, maybe sooner, maybe later” fit.
Good luck to you, OP. I think your good question helped you dodge a bullet on this saddle.