How can I break into Private Equity ?

Hi guys, 

French from a semi-target school here (think EDHEC/EMLyon). I did two internships in IB : top EB (Roth/Laz) and top tier French bank. I'm only in the first part of my penultimate year - I'll do a second internship starting in January 22 for 6 months.

I really want to break into PE (the biggest fund as possible) as full time position after graduation without the "classic track" of 2/3 years in M&A at BB, and I know that competition is quite fierce. So I was wondering : should I keep on completing internships in IB, with the next one at BB (January 22), or should I do the next one in PE but in a middle tier one ? Saw that students from my school with a similar resume did at Eurazeo for instance and Mega funds or top tier funds seem totally impossible to get. 

In case I go for PE as next internship, which fund can I aim at and having chances to get the offer ?  

Thank you for your comments and advices :)