No, its nothing to do with the exhaust.I have just had the same problem on my bike which is a 2006 HONDA CBR 125R.
On start up i pulled the choke out (on a cold day) while keeping the throttle on the engine is suppose to tick over but didn't. The engine kept cutting out.
The problem was the carb. There was alot of air in the fuel tank, and where the fuel tank is theres a pipe which carries the fuel to the intake on the carb which then carries the fuel to the jets in the carb. It was the air that was blocking the fuel from entering the jets. So i took it into the dealers because its a big job plus the have to re-tune the carb after fixing. That will be the answer. Take the bike to a PEUGEOT DEALER asap to avoid serious damage to the fuel injector. Warranty might not cover it. The last bike i had was a 2005 PEUGEOT Jetforce 125(efi abs) model and had the same problem like you have but my speed was cut to 6mph, and the warranty wouldn't cover the repair so i had a bill of £150.00p. Not many people in the UK own a peugeot now after the problems especially what i went through. This is a kind suggestion. (GET RID) Had problems with mine well before the first service was due. Including FUEL INJECTORS, IGNITION BARREL, AIR INTAKE etc. Theres a bad customer service reputation with Peugeot motorcycles, mine covered 10,000 miles. The exhaust was another problem i had. The (BAFFLER) inside the exhaust was loose, so i told Peugeot and they said they will not pay for the replacement, so i threatened them with legal action. So then they replaced it. If you want anymore information on PEUGEOT then go to www.reviewcentre.com. All the ex-peugeot bike owners are on that site. Type peugeot scooters. I now own a HONDA CBR 125 and the bike has never let me down,never.And it's now covered 12500 miles. Just looking out for your sons safety. BEST OF LUCK GWJONES
G W JONES
April 2008