If you want breathtaking views of the French Alps while getting to enjoy the luxury and immense fun of a mountain bike, this is definitely a must visit destination
From Chamonix, it is very easy to get to Le Tour. You can either drive up the valley, bike up the valley or take a cheap shuttle that runs every 15 minutes up and down from Chamonix to Le Tour, and everywhere in between. I took a shuttle up the valley to Argentière where I rented a bike from the shop, Namaste, and biked myself the rest of the way (1.5 miles or so). If you are confused any local in town can explain how to get yourself there with ease.
Le Tour is a ski resort in the winter just outside of Chamonix that offers lift assisted mountain biking in the summer months. It is only 20 euros for a full day lift ticket with unlimited carries to the top with your bike.
There are two lifts operating in the summertime. Once you get off the first one you can either ride down, or opt to go higher up on the second one right in front of you. I recommend getting all the way to the top for the views. From there you have a multitude of options. You can begin multiple cross country rides which can take you into Switzerland and other Alp regions, you can keep riding up toward Mont Blanc or you can enjoy all of the fun downhill trails.
Since I was only here for the day and I was alone, I rode mostly the downhill trails and they were all phenomenally fun. I didn't specify a distance for this ride because it depends completely on what you make of your time here. If I had more time in this area it would be really cool to embark on a bike-packing trip through the Alps here, because these trails to connect you to many other systems in the area.
On the downhill trails there are a couple places to stop and grab a beer or a snack on the mountain. It was great taking a break and enjoying the views of Chamonix below me, the massive peaks above me and the rolling green fields full of wildflowers surrounding me. An absolutely gorgeous place to be able to ride a mountain bike!