My research led me to Bike Basque, a tour operator based in Biarritz. Its one-week “Raid Pyrenees” itinerary takes cyclists from France’s Atlantic coast to its Mediterranean shores, tackling one of Europe’s great mountain ranges on the way.
What it lacked in length (around 450 miles, compared with 874 for Land’s End to John O’Groats) it made up with steep slopes (16 major ascents and 40,000ft of climbing). A reasonable substitute.