Ah. Several new posts while I was typing mine.
If you consider that your child has special needs, this may actually give you a strong case at appeal. Children with special needs who are admitted outside the usual admissions round are one of the very few (7) exceptions to the infant class size regulations. Is your child already receiving support or care from a health care professional or psychologist? If so, you should present evidence of that. Be aware, though, that it will not be enough to state "my child has special needs"; there has to be confirmation of that from a professional and there has to be clear evidence that your preferred school has expertise or facilities which aren't available in other schools, as all schools are expected to cater for children with a range of needs.
On social and medical need, the School Admissions Code says
Social and medical need
2.27 If admission authorities propose to give higher priority to children for social or medical reasons they must ensure that in doing so they are not failing to comply with paragraph 2.16(g) of this Code, which prohibits the use of oversubscription criteria that discriminate against or disadvantage children because of their special educational needs or disabilities.
2.28 Admission authorities must not use this criterion to give a child a lower priority in obtaining a place at the school, but it is acceptable to give higher priority to children or families where there is a social or medical need (for example, where one or both parents or the child has a disability that may make travel to a school further away more difficult).
2.29 If using this criterion, admission authorities must give a clear explanation of what supporting evidence will be required ? for example a letter from a registered health professional such as a doctor or social worker ? and how this will be assessed objectively. Admission authorities? decisions must be consistent and based on this objective evidence. The supporting evidence should set out the particular reasons why the school in question is the most suitable and the difficulties that would be caused if the child had to attend another school. Admission authorities must not give higher priority to children under this criterion if the required documents have not been produced.
2.30 This criterion, if used, must not relate to particular aptitudes for some subjects such as in sport or music. For example, schools must not seek to admit children, under this criterion, on the basis that they ?need? to attend the school because of an aptitude or interest in sport and the school has particularly good sports facilities. Selection by aptitude is dealt with in paragraphs 2.78 to 2.82 of this Code and schools wishing to admit a proportion of children on the basis of their aptitude for a particular subject must follow the guidelines provided.
It seems to me that para 2.30 means (by analogy) that a school could not admit your child on the basis that s/he 'needs' French tuition, just as it could not admit a child who 'needed' sport or music. That is something that you will have to test at appeal.
The school admissions appeal code is available at the same link but I can't get it to open. You should check what that says about social and medical need.
Finally. The Ministry of Justice has published a Guide to the Human Rights Act. On page 20, it says
For example:
? It might not be a breach of your right to education if the state does not provide a particular kind of teaching. But if the state provides it for boys but not for girls, or for people who speak only a particular language, but not another, this could be discrimination in relation to the right to education. If this was your case, you would rely on your rights under Article 14 (nondiscrimination) taken together with Protocol 1, Article 2 (education).
On page 27, it says
Limits on the right to education
3.121 The general right to education is not an absolute right to learn whatever you want, wherever you want. The Government has made a special reservation to the ECHR in this area so that education provided by the state is limited to the extent that this is necessary to provide an efficient education and within public spending limits. You might not have a right to the most expensive form of education if there are cheaper alternatives available, but the Government or local education authority must balance the right not to be deprived of an education against the spending limits it imposes. The Government has stressed that the cost of providing education is a relevant factor in making these decisions.
In a recent case it was also held that the duty under Protocol 1, Article 2 was imposed on the state and not on any particular domestic institution. It did not create a right to be educated in a particular school or a particular manner, so that if an expelled pupil was able to have access to efficient education somewhere else, there would be no breach of his or her Convention right.
All the bits I've highlighted suggest to me that your argument that your child has a right to French tuition at your preferred school will get nowhere. I don't usually recommend going to a lawyer (and taking a lawyer to appeal hearings can backfire on you) but if you are determined to quote the Human Rights Act, you might do well to seek legal advice. You could also seek advice from the Advisory Centre for Education.