Northeast of Chamonix near Argentiere, the Lognanmountain bike route is a switchbacked doubletrack from Le Plagnolet/Gare parking area (1252m) in Argentiere up to the Lognan summit (1972m).
For an easier time, take the Grands Mtets cable car in Argentiere to the mid station (Lognan). From Lognan station, the track is the home piste in winter. Exit the station and turn immediately left. Its very wide but extremely rough all the way to Argentiere. It drops 800m but feels like 8000m. Your bike may not survive the beating it will get.
Alternately, try riding from Lognan to Le Lavancher. From Lognan take the first right 4x4 track which heads off towards Plan Joran. The 4x4 track eventually leads into a large bowl with views of Chamonix. It turns into a small walking track, then exits the plateau to start the descent into Le Lavancher. The track is technical with many zig-zags.
Overall, Lognan is the 41st most popular mountain bike trail of all 104 mountain biking rides in France.