You’ll get to the Life Support area of Talos 1 during the "Reboot" main story mission. As soon as you enter the area, you’ll have a few choices about where to go. To pick up the "Missing Engineer" optional objective, you have to go up the stairs on the right side of the first hallway you enter.
The security booth requires a keycard to access. It can be found in the nearby bathroom. At the back of the bathroom, past the stalls, there’s a grate on the floor that can be lifted with Leverage 2. You’ll find the Security Office keycard in the vent underneath.
The computer in the security office has an area map to download, and an email about Jean Faure.
Locate Jean Faure
While you’re at the computer in the security office, use the crew tab to pull up Jean’s tracking bracelet — we’ll walk you through where to go, but having the marker on your HUD will help a lot.
You’ll find Jean’s body in the large Reactor room you explore during "Reboot." There’s an elevator shaft on the far side of the room from where you enter. The door to the elevator shaft on the top level of walkways is locked, so you’ll have to go down one level. Stand on the edge of the platform and look up — you’ll see an maintenance access tunnel. That’s your goal.
Build yourself some GLOO platforms to climb up to the tunnel. You’ll have to handle some typhons when you get inside. Jean’s body is at the end of the hallway along with a suit chipset and a neuromod.
Finding Jean is only the next step in this objective. To complete it, you need to take the Atmosphere Control Room keycard from her, then go there.
Access the air filtration control room
The keycard you just looted from Jean’s body is for a locked room in the Atmosphere Control room in Life Support. You’ll have to backtrack a bit to get there.
When you get inside Atmosphere Control, take the stairs on your left. Go into the Air Filtration Control Room, then through the locked door on the left. This completes the objective. Before you leave, make sure you loot the neuromod from the locker.