Best snow for late season around Geneva

This may be a dumb question

I am a newbie to all things Alps and planning a trip for last week
of March and first week of April. I know things could probably change
a lot between now and then but I am finding it overwhelming to research
which mountains in which regions are getting more snow and which ones
to avoid this season.

I will be coming in to Geneva from Paris so mainly looking in the French alps
and western Switzerland.

I am an Intermediate - Advanced skier so probably won't be hiking up for steeps or anything but want some decently challenging
trails.

Well, no one will be surprised if I mention Verbier: If you're on the train, then you could carry on to Martigny, change to the local train to Le Chable, and then get the lift up to the resort (or even stay in Le Chable). If you're on the TGV, you may even be able to get to Martigny direct, without changing at Geneva. You can also get to Chamonix by train from Martigny, but I've no idea how long this takes.

Look at http://www.sbb.ch to see the logistics of the trains and gondola connections for the time that you're travelling. There are also verious offers available from the Swiss Tourist website at http://www.myswitzerland.com/en-gb/service-updates/affordable-switzerland-1.html. I've seen a combined rail and liftpass offer for Verbier recently, I think on the Verbier website at http://www.verbier.ch

Verbier will be running as longs as it can, but if the snow is going then they will start to close some of the lifts/pistes. The town itself is at 1500m and as with any high resort late in the season, you'll be dependent on the local conditions as to how much of the place in accessible.

Verbier is offering a 15% accommodation reduction at the moment.

Verbier is very expensive but a superb resort.
Alternatively you have Flaine and Morzine nearby to Geneva for short transfers and slightly lower costs.

I would say zero chance of real powder if you are not willing to walk. Rent some skis with touring bindings and you have a chance.