Over the next few days the weather in the Alps will be quite mixed with some snow here and there but generally not in a huge quantity. It will stay quite cold though, which means that any snow will fall well into the lower valleys. The northwest and southeast of the Alps will get the most precipitation this week. Towards the middle of the week, Wednesday evening to be more specific- it will become warmer in the Alps and Pyrenees before cooling down again from Sunday.
The sun will come out in the French Alps on Monday, but it will continue to snow in the east of the Alps. Tuesday starts bright in the western Alps, but there may still be some clouds with some tailing precipitation in the far eastern parts of the Alps. The sun will start to shine over there as well. It might snow a bit in the northwest in the night from Tuesday to Wednesday, but there is plenty of sunshine again on Wednesday. You can expect 20-35, locally 50 cm of fresh snow between Sunday afternoon and Tuesday morning. The ski resorts in the Pyrenees will benefit the most.
The jet stream keeps on coming from the west next week and new storms will find their way to the Alps. The wind turns to the south when the new storm comes in on Wednesday and the northern Alps will temporarily have to deal with a southern Föhn (. Thursday will be mild and what happens next is still uncertain.
After record breaking snowfall last month there is a remarkable amount of snow in the Northern and Southern French Alps. Snow conditions in both the Alps and the Pyrenees are generally excellent in the busiest week of the season, with no real week points anywhere, at least on-piste. Conditions are more variable off-piste but there is still some excellent skiing to be had, even some powder, especially in the Pyrenees.