...Bison Futé is the French gov. website for national traffic conditions, so that will tell you.
Edit to add, website don't seem to be working at the moment, says something about back on by April 15th. but once its back up & running it does give real time traffic updates for all of France.
Alternatively just check French weather website if its showing snow up there then probably best avoided unless you have winter tyres/snowchains.
Not just winter you need to be concerned about. We were at Pyrenees Natura last year in June and most of the passes were closed even then due to the very bad spring they had (same as we had in GB). We were lucky in a way as with the mountains covered in snow it was absolutely spectacular (even though we couldn't get to the Pic du Midi or one or 2 other places).
As ValA says there are always notices on the roads to the passes (in our case even in June) to say whether they are open or closed.
Couple of shots to show what it was like even in June. Yellow sign on the first is "Route Baree" just above Lac d'Estaing just above Pyrenees Natura campsite. Second is when we set off for Pic du Midi and couldn't get through and the avalanche / snowslide shows the problems with the passes.