Ahh I think that minigame is bugged for me
It is a bit buggy yes, i simply continued trying until i got it solved.
The main problem is, that it is not really clear when you have to click for the ball to open and even if you just click all the time, the ball sometimes opens and catches your prey and sometimes it does not (most of the time).
I thought her health is important but that also is not the case, sometimes the ball opens when her health is at 10% and sometimes when it is 90% and again most of the time it does not, no matter her healthbar.
So timing does not help, clicking on the ball instead of the girl does not help, her health does not help, not clicking often or clicking like a madman also does not seem to have any impact on the chance. Pure randomness it seems to me.
You need to catch every of the 4 girls once for Jean to appear (for each girl you catch get a pokeball at the top of the screen) then you can catch Jean.
You cannot lose the minigame so it only takes time.