I am a UK national. Can my non-EU wife be deported when we both live in France and I am a worker paying taxes, holding a French driving licence, a Carte Vital, self employed and also have a French contract job for the next 3 years?
Yes, but only under very limited circumstances that would not be applicable to most people.
Under directive 2004/38/EC, your wife can be deported only if she is a threat to public safety, health, or policy. This is particularly a consequence of Articles 3 (section 1) and 7 (sections 1 and 2). Provisions concerning expulsion are found in Chapter VI.
Another possibility that could lead to her expulsion is a finding by the French government that your marriage is not genuine, or was undertaken as a marriage of convenience (Article 35).
Until March 29th, EU freedom of movement allows you as a UK citizen to move to any EU country except the UK with your wife, and to many EU countries with your husband (assuming you are male). There are some formalities to meet, which is not difficult or expensive.
Nobody knows what the situation will be like after March 29th. It is reasonably likely that she will be Ok until the end of 2020; after that you'll have to see. Welcome to Brexit.
And the UK has deported women from the UK that were married to a UK citizen, and mother to a British child, all living in Britain.