does anyone knows what happened between michael and nikita in the original series "La Femme Nikita" ?

Well I'm only on season three so I can't tell you everything.. but Nikita was recruited by Section One much like Alex, even their first meetings with Michael are similar (waking up, being told you're dead in the real world etc.)

Michael and Nikita have a very complicated relationship. Michael in LFN is much more stoic and hard to read, we never really know how he feels about Nikita, epsecially in the earlier seasons. There are times when it seems like he deeply cares for her but then he betrays her to do sections bidding. So, it kind of gives their relationship a love/hate vibe.

If you want to check out some episodes I know a place with some links. You can message me if you want.

Just as Wishful Thinker stated, the CW show has remained pretty close to all versions including the USA. Just like the CW Nikita-Michael, Alex-Thom relationship, the USA Michael watched over Nikita while remaining loyal to Section One. Additionally, just like the CW's Michael, despite direct orders to place her on suicide missions, he frequently warned her and helped her to escape. However, when Roy Dupois left Nikita after season 4, they brought in a new partner for Nikita. But, Roy Dupois did continue to guest star in Season 5.