ECU Failure ? How to test ?

Would appreciate any advice ~

I have a Ref 2003 Peugeot 206 1.4 petrol engine with a Sagem (9646988680 / s2000A) ECU

The car starts first time and runs ok - except for a slight intermittent misfire and high emissions in the form of wisp of black smoke when it starts - this reducing but not completely going when driving. The car drives well at speed, has power, does not stall and the slight misfire is hardly noticeable when driving

I can probably resolve the emissions and misfire with new air filter, Co2 / MAP Sensor and Coil pack ~ but there is a fault with the ECU that I would appreciate some advice with

When ignition is turned on on the dashboard ECU light comes on ( which it should ) ~ The ECU light goes off when the engine starts - and stays off, even when the Co2 & Map sensors are disconnected - which is a fault which should show an ECU light on the dash board ?

So the ECU is not showing these faults ~ as ECU dash light stays off when engine is running and shows no faults indicated when connected to a diagnostic tool?

Has the ECU failed ?

Many thanks Dave