I assume you mean a Peugeot 307 as the 308 didn't hit the UK market until 2007.
"I would start by checking for any vacuum leaks in the plastic pipework for the inlet manifold, brake servo pipe etc: It is common for these to crack when they become brittle and this will cause the engine to run lean. Next is to take throttle body off and give it a good clean with carb cleaner or brake parts cleaner. With age, the "throttle plate" and inlet throat get gummed up with a sticky carbon residue which can cause the butterfly to stick a bit, especially at idle where it is nearly closed."
At 10 years old in 2015 the timing belt is due for renewal next year.