The longest black piste in Europe as well as in the whole world is the Sarenne piste in Alpe d'Huez.
It's on the piste map (from the Alpe d'Huez home page) stated as 19 km but on the Alpe d'Huez home page it says 16 km so the actual length is a bit unclear.
It can be noted that last part of the piste (which is several kilometers) after coming down to the bottom of the Sarenne gorge is more transport than black.
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There actually seems to be several candidates to the title:
1) Vallée Blanche in Chamonix from Aiguille du Midi down to Chamonix. There are several different numbers given for this run between 20 and 22 km. The Chamonix home page claims 20 km. Note that this is not a piste, it's a commonly used off-piste route where a mountain guide should be used.
2) From Kleine Matterhorn to Zermatt. Ski-zermatt claims 13 km and zermatt home page claims 22 km.
3) The Sarenne run in Alpe d'Huez is often claimed as the longest piste. It's on the piste map (from the Alpe d'Huez home page) stated as 19 km but on the Alpe d'Huez home page itself it says 16 km so it's probably not the longest piste but it is the longest black piste, even though the last part of it is more transport than black.
Longest ski run in Europe also means longest ski run in the world.
The highest skiing is at Gobba de Rollin in Matterhorn ski paradise which is at 3899 m.