[JSEL]

Iv had pretty similar problems with my Clio same as yours just a with a manual gearbox. Although mine didnt vibrate before it cut out(might be because yours is a automatic, no experience with them :/), would lift off the accelerator at junctions and it'd just slowly die until the revs dropped and it cut out.

When you started it back up did you need to keep the revs high for a few seconds to prevent it cutting out again?

Does the coil light only appear when the car cuts out? If not then it could possibly be a wiring loom problem causing the car to get mixed signals.

Also if you can open the air filter housing and see if there's any oil present in the airbox/ intake manifold. This usually causes the throttle body to stick hence the stalling. Its pretty easy to clean, but if there's oil in the intake manifold it usually means the Rocker Cover needs replacing(Not an expensive fix).

Also a few threads, just incase uv not came across them i found useful:
http://www.renaultforums.co.uk/showthread.php?t=68736
http://sandpit.no-ip.com/clio/

Hope this is of some help to you, im not an expert by any means just sharing what iv gone through with my clio