Because many other people have answered these kind of questions better than us, we've put a very succinct answer here and then a link to another site which answers the questions in more detail.
Why home educate?
Because each family is unique, each family will have their own unique reasons for home educating. A common theme is to be able to give the child greater freedom of choice and create a learning environment which will suit his or her personal needs. These may be special needs, resulting from having dyslexia, ADHD, Aspergers or Autism amongst other things, or the needs that arise simply because each child is unique.
We personally feel that the school system is lacking in several ways, creating problems such as bullying, over-pressurising children with endless tests and truancy.
In the home (and library, park, friends house, garden, museum and all the other places where learning is possible) it is possible to give nurturing, one-on-one support which just isn't possible to the same extent in school.
How to home educate? Or, could I really do it?
We practice a form of home education called Autonomous Learning, where the child is presented with a range of 'learning opportunities and experiences' but is not forced into learning from a standard curriculum. This is very different to permissive parenting, our children have fixed boundaries when it comes to behaviour, we just feel that learning only truly takes place as a result of joy and interest in a subject. Children have a natural craving to learn - to find out how the world around them works, to ask why? to learn to read books for themselves, to be creative and exploratative. It's part of being a child.
The school system was initially set up by well meaning folk to keep children relatively safe from harm as they grew mature enough to exploit, They decided to teach children how to read and write, maths was soon added and as it became clear that reading, writing and arithmetic did not take all that much time, other subjects were incorporated into the curriculum like some sort of padding, and like padding it's often completely forgettable or useless.
If you can read, write and do some very basic arithmetic, you can home educate your children. You do not need a te
aching qualification or anything like that, you can let your instincts guide you and seek support from other home educators. There are some other things you do need. You need to enjoy spending time with your kids, be willing to play with them and learn with them and have a fair amount of time - home education is a life style choice and if you are willing and able to make it, a very rewarding one.
For more information on Why and How see the Education Otherwise website.
What about socialisation?
Socialisation comes easily and naturally to most children, particularly those who have never been to school. Home educated kids get to play and socialise with other homeschoolers at any time, school friends in holidays, evenings and weekends and also adults. In many places there are strong home education networks which organise regular events and there is nothing to stop a home educated kid from joining a regular sports, musical, acting, etc. class.
I believe that school encourages (you could even say enforces) children to play only with other children their own age or gender. From spending a lot of time with both home educated children and school children, I have noticed that the home educated ones are very happy to play with other children of all ages and also know how to communicate with adults. They are not intimidated by strangers and are happy to ask questions and chat to everyone.
Learn in Freedom details information about research done in this area.
Is it legal?
In both the UK and France, the short answer is 'yes'.
In France home educators are required to register at the local town hall either in person or by mail whichever is easiest, and with the Inspection Academique once a child reaches the age of six. The Inspection Academique will expect to see the child either at their own offices or in your home once or twice yearly to meet up and discuss how you are educating the child and talk to the child him/herself with you present.
This is recent development - previously twice yearly tests were carried out which measured the child's development (as opposed to a comparison to a school child), with a focus on written French and maths. In the department of Aude (11) where we live, this has now become much less formalised, provided that the parent's demonstrate that they are providing the child with an education, no test is no required until age 11.
I hope this trend is spreading nationwide, but we can only speak for our own experience and the experience of several other home educating families in the Aude and nearby areas. It's worth noting here, that the changes that came about in our area were due to one parent standing their ground when they discovered there was no legal requirement for a child of 6 to 11 sitting for 3 hours in a room answering test questions! Once the facts were established the Authorities backed down and are now happy to meet home-schoolers on our terms.