It's all to do with the viscosity (resistance to flow) which will also affect the boundary lubrication (fine film of oil that clings to components) if the engine grade isn't right in can affect these fine tolerances and not lubricate the engine sufficiently
The problem with a 5w40 on a decade old engine is that the fine tolerances you are talking about are now all a lot less fine than they used to be, so as a result an oil with a slightly thicker cold grade will allow you to generate pressure in fewer turns of the crank when cold starting.
So like I said, the 10w40 is probably preferable now that everything is worn.
Also you have to remember that oil dilution from fuel becomes more of an issue over time when the rings are worn, so this leads to a breakdown of the oil, so when you first put your 5w40 in it might be working ok, but at the end of its 10K or whatever stint in the engine it will be fuel diluted more than was intended on a new engine.
Amazingly in this case apparently even renault have worked that out which I must admit surprises me as normally they know naff all about their own engines, lol