Full time employee to my company is working for another company at the same time

I have an employee in France who has not been turning up for work, taking calls etc. He was warned and put on notice, and I have just been made aware that he is working for another company as a consultant which is breach of his contract with us. When he is supposed to be working at our office and does not turn up he is at there office and when he is supposed to be working from home for us he is working for the other company. Can I terminate his contract immediately thus meaning I don't have to pay his remaining 2 months notice?

[AFFA]

I wish to inform you that you may terminate employment of your employee. In this regard you may first issue a notice to your employee to explain his conduct of causing breach of contract and may further specify in your notice that as he has caused breach of agreement by starting working with some other employer therefore if he fails to provide explanation then his employment will be deemed to be terminated by him because of his conduct and after this you may terminate his employment.

AFF