There are glaciers as soon as you go inside the range, therefore you also have to be prepared and equiped for crevasse safety.
A very famous area is the Glacier Blanc leading up to les Ecrins (4000m+ at the Dôme), a superb summit that is relatively easy to ski. And on the sides of the glacier there are plenty of other nice peaks. There are 2 huts along the glacier, Refuge du Glacier Blanc and Refuge Caron, you may spend 4 days in the area without getting bored on very skiable slopes, usually no difficult climbing involved.
Another very scenic tour lasting about 4 days is around la Meije (a few meters short of 4000m but you won’t ski this one, only admire it!). It goes through a series of saddles and passes, with different options and huts, but couloir skiing and possibly abseiling is on the menu, more mountaineering experience is needed than for the Glacier Blanc.
And they are many other possibilities!…
Last but not least, the best time is usually more April and May, March might be early in terms of weather and snow conditions.
If you wanted to go step by step you could also spend half of your time in nearby Queyras as a warm up (superb mountains for ski touring, no glacier, huts in villages, exceptional weather) and then move up to Massif des Ecrins.
Agneaux on the left, Ecrins on the right, seen from the North.
Ecrins on the left, La Meije on the right, seen from the North.
Queyras, paradise for ski touring