Two bits of good advice from Noel so far.
As he says, if the indicator switch isn't self-cancelling, then the switch is faulty. Not much help for Liam, but a good place to start for Service C, as the switch will need replacing anyway. You could be lucky and find that this also fixes the indicator fault, or you may be unlucky and left looking elsewhere afterwards.
I'd also second Noel's original comment regarding the hazard light switch. These are notoriously problematic on Renaults, and the normal indicators will probably be wired through the hazard light switch too. It's a relatively easy part to change and shouldn't cost too much.
The worst case scenario is one I'm not keen on at all. I'm not sure about the 99 model, but on an 03 Clio, the indicators will be controlled by the
. If that's gone faulty, then it's an expensive bit of kit to replace. You can't buy second-hand, and they have to be coded to the car by someone who has the Renault diagnostic computer.
Just one last thought. It could be one of the plugs into the
that's loose. I think they're accessible from the front passenger footwell, over towards the door.
Give the plugs a good jiggle (or disconnect/reconnect if you can) and see if that helps.