Le Savoy
The Savoy nursery ski area has a very gentle gradient and the pistes are nice and wide, allowing you practise turns and build confidence before heading higher up the mountain. There are two drag lifts here that you'll need a ski pass for and a free magic carpet lift.
There's a small cafe near the big drag lift for when you're ready to take a break too.
If you're skiing in a group with mixed ability, the beginners can practise at Le Savoy, whilst the more accomplished skiers can head up on the Brevent gondola to the main ski area, meeting up easily later in the day as the home run from Brevent leads into the top of the Savoy ski area.
Les Planards
Les Planards is the bigger area of the two nursery areas in Chamonix centre, with short drag lifts (one short and one long) and a gentle gradient green piste to build your confidence on.
When you're feeling confident on the green piste, you can progress to the longer drag lift, hopping off half way where you can start making turns on slightly steeper terrain. The next progression after this is to take the long drag all the way to the top.
There's also a two-person chairlift accessing a steeper blue piste and a red run for those who are ready to progress. A restaurant with a large terrace offers the perfect place to take a break, or to join non-skiers in your group.