2004 Jaguar X-Type mis-fire and smokey exhaust

It is most definitely running way too rich, this could by bad O2 sensors or leaky injectors, Jags are famous for the injectors, if you do it do all at the same time, but read the codes and check fuel pressure and do an injector leak down test.
Also:
First thing you need to do is have the codes read, Autozone does it free, Post the results with the code number(s). Even if the service engine light is not on, there should be freeze frame data stored.
If it won't make it to Autozone, buy a cheap scanner, they can be had for 30-40 dollars, a good investment, since they cover all cars sold in the USA from 96 on.
If the light is blinking, it means engine misfires possible damage to the Catalytic converter. Service it right away!