I have read on other forums that Clios can have a habit of developing intermittent earthing problems. Even if these cables look solid they need to be pulled to make sure that the crimped terminals are secure and that the terminals are making a good electrical connection.
Either from the battery lead to the chassis or perhaps from the chassis to the engine block.
The Haynes manual suggests ways to test for an earth fault.
If you are lucky enough to catch the problem then you'll need a volt meter to trace back earth connections.
In other posts I have seen mentioned problems with the 1.6 16v Clio's 'little black box' on the bulkhead at the rear of the engine. It "protects" wiring before going into the
and can rattle free and destroy the wires it is protecting! However, this may not be a problem on your car.
Perhaps, when the towman puts jump leads on, then the voltage and current is just high enough to overcome the intermitent connection.