Time for a Kevin Bacon EE impression...
Lausanne has replaced Rennes as the smallest city in the world to have a full metro system, and both systems utilise rubber tyre technology.
If you were to travel by public transport overland between the two cities, a popular route would be from Lausanne - train to Paris Gare de Lyon, line 14 Metro to Ch^telet, line 4 Metro to Paris Montparnasse, then train to Rennes.
Both metro line 4 and metro line 14 also utilise rubber tyre technology, and thus provide a "link" between Lausanne and Rennes through the French capital that is consistent with both cities own metro systems.
Therefore the answer is rubber. Probably. Or maybe not.
It is also worth noting that the original 1991 Lausanne M1 light rail line terminates at Renens, which is an anagram of Rennes. Employees of Metrotram took this one stage further by creating their own direct link between the two cities in the "Chronology" section of this
link...