The short answer is yes (but only recently)
The Freedom of Information Act only applies to bodies which are listed in the act itself.
Under New Labour, that did not include academies. The Government resisted adding them to the list.
However, through the Academies Act 2010, the Coalition Government has added Academies (and by implication free schools) to the list in the Act.
That means that, like any other body covered by the Act, they must comply with requests for information unless one of the reasons given by the Act for refusing information applies.
The most common basis for refusal would be where the information relates to personal information about named individuals. But that is no different at an Academy to in a maintained school.
Generally, an academy or free school would thus be required to provide copies of minutes of governors meetings, financial information, and so on.
If an academy or free school refuses your request for information, you can challenge by complaining to the Information Commissioner. His web site contains lots of useful information about what you can ask for, and when they can refuse.