Non-EU married to a British citizen. Must we travel in Schengen zone together?

I am an Egyptian man living in Egypt. My wife lives in the UK. We were planing on go on holiday to France. Is it possible for me to travel to France as an EU-Spouse without needing a Visit visa, or does she have to come and take me with her and enter together France?

You can travel to France as an EU spouse, but you will need a visa. The visa is free of charge and can be refused only if you are found to be a threat to public health or safety, or on grounds of public policy. To use this visa, you must arrive in France with your spouse, or after her. It is therefore not necessary for her to travel to Egypt.

If you want to go to France before she arrives there, you can do that, in theory, but you would need to have a regular Schengen visa. If you apply for a Schengen visa, you have a much higher chance of being refused.

My wife would leave back to UK. Do I have to leave France as well or can I stay for more time[?]

Once your wife leaves France, you no longer enjoy the right to stay there under European freedom of movement rules, so you would probably be best off leaving.

and if I can stay for more time how long I can stay[?]

There's not much in the rules to cover this eventuality explicitly, however, so it's not possible to say precesely when you would have to leave, or what would happen if you left after your wife did.

and what if I wanted to work there as well until my wife finish the spouse visa[?]

It's not clear what you mean by "until my wife finish the spouse visa," but I will assume that you want to move to the UK. You are allowed to work in France if your wife is there, but not if she is in the UK (since you aren't supposed even to be in France as an EU spouse unless she's there with you).

If your ultimate goal is immigration to the UK, you might be able to benefit from the so-called Surinder SIngh route. To do this, you would move with your wife to France or another EU/EEA country for at least six months. After that, you would be able to move to the UK under EU freedom of movement rules instead of under the immigration rules.

If you are interested in learning more about that, you should visit http://expatriates.stackexchange.com. There are already several questions and answers there concerning EEA family permits. Any questions you might have about moving to France, or to the UK, or anywhere else for that matter, should be asked there rather than here.