Drawing shows the 1.4 Petrol (1360cc) parts - other models are different.
The original exhaust systems (including the oxygen sensors) appear to be trouble-free on these cars. After 7 or 8 years, the rear exhaust box may need replacing and this is a straightforward job for the local exhaust specialist.
More recently, I have needed to replace the 16 year old centre exhaust on one car - check if you need a fitting kit 1797.74 first, as it includes a special "slippery" gasket. If the old one is refitted, you may get odd squeaking noises as the exhaust tries to flex.
Drawing shows the 1.6 Petrol (1587cc) manifold and catalytic converter - other models are different.
These can rust out after a long time - but can be replaced - see ebay advert or search for "Peugeot 1007 rear silencer exhaust strap". It would be a good idea to spray with a can of heat-resistant spray paint as the sides may not be treated so it could start corroding again - - - -
Alternatively, this is an aftermarket rear exhaust - the hanger is welded directly on to silencer.
No noticeable increase in sound levels - works well and cheaper! Fitted June 2014 and still OK seven years on
The average age of catalytic convertor is 10 years, what would be the most accurate way to isolate a faulty or partially blocked one in a 1007?
I've not heard of any needing changing on the petrol models so far - they do seem to go on and on. Unless the engine light is on, leave well alone.
If the engine light is on - then
Only once these are all checked and cleared, then look to the O2 sensors and/or catalytic converter
My view only - others may have better solutions.