Sounds like your speedo sensor has gone - replacement is about £30 from Renault and takes 10-20 minutes to fit. The downside is that you need to be able to get into the engine bay as it sits near the gearbox - this is much easier if you can get the car on a set of ramps or similar.
These sensors are prone to damp, which can cause the speedo to shut off intermittently. The contacts on the sensor can be cleaned, but it's easier to just replace the whole thing - on Mk2. Clios at least, the sensor clips into place. Further, if the speedo decides to go to sleep, the engine management light will come on if the engine has been running at 3000rpm+ for more than 4 minutes if the ECU hasn't received a signal - however, there don't appear to be any fault codes logged in the ECU in this case, which is where the 'no fault' diagnosis may be coming from.
Nice tip about the clock test mode - will have to remember that!
Whoever said the entire instrument panel needs replacing is talking BS, I'm afraid.
root-two, December 2008