I am a french citizen and my wife is Japanese.
Although she is a french resident, she has not got the french nationality.
She has a work permit in France.
She would like to work in the UK, but the employer told her she needs
A EU work status.

Does she have this status automaticaly because her husband is french?
If not, what does she need to do in order to get the EU work status?

Nationals of any country that is not a full member of the EU, EEA, or EFTA, MUST obtain a Work Visa or Permit to work in the country where the job is located PRIOR to taking up employment.

So the employer is correct !

How to Get an EU Work Permit (http://thetravelersnotebook.com/featured/how-to-get-an-eu-work-permit/)

Success !