I am applying for a French visit visa or Schengen Visa. When I answer yes (to the question "A close member of your family is A national of EU?") to confirm that my brother is an EU (British) citizen, the next answer regarding ‘job’ vanishes. What does that mean?
The question about whether a close member of your family is a national of an EU country is almost certainly supposed to identify whether your visa application qualifies for treatment under the EU freedom of movement directive (2004/38/EC). For applications under the free movement directive, information about employment, income, and the like are irrelevant, which would explain why the job question vanished.
Unfortunately, it seems that the application may be poorly designed in two respects.
The first is that a Schengen visa application only qualifies to be assessed under the free movement rules if you are traveling with or joining your "close" EU-citizen family member, but there is no indication that that is the case here.
The second more significant fault in the application is that they haven't defined "close family member," which presumably is meant to invoke the directive's definition of "family member" at Article 2(2), perhaps also intending to include the provisions of Article 3(2)(a). It's not particularly reasonable to expect you to know the applicable definition, but I suppose that people who work in immigration matters forget that relatively easily. The definition generally does not include siblings. An exception to that rule would be siblings who are members of the same household (Article 3(2)(a)).
If you are not traveling with your brother, or if you are traveling with him but do not live in the same household, you should answer no to that question. To avoid the appearance of deceptive intent, you should include a statement about your brother in the application, wherever you can add additional information in free text form. The statement should note that your brother is a citizen of the UK, but that you answered "no" to the "close member of your family" question because you saw that the question was asked in connection with the free movement directive, and your application is not for a free movement visa.
On the other hand, if you are traveling with him to (or joining him in) France, and you are members of the same household, you should answer yes to the question and be unconcerned that you cannot enter information about your employment.