Instead of using JSONObject you may use JSONArray. If you really need to convert it to a List you may do something like:

List<JSONObject> list = new ArrayList<JSONObject>();
try {
    int i;
    JSONArray array = new JSONArray(string);
    for (i = 0; i < array.length(); i++)
        list.add(array.getJSONObject(i);
} catch (JSONException e) {
    System.out.println(e.getMessage());
}

The original "list" is not well-formed JSON. Perhaps you meant the following:

[{"a":1, "b":2}, {"c":3, "d":4}, {"e":5, "f":6}]

If it is in a file called testFile.json, you can import it as JSON:

jsonLst = Import[FileNameJoin[{"path", "to", "testFile.json"}], "JSON"];

If the snippet is a string called str, you can import it as follows:

jsonLst = ImportString[str, "JSON"];

In either case, you will have a list of lists of rules:

(* jsonLst = {{"a" -> 1, "b" -> 2}, {"c" -> 3, "d" -> 4}, {"e" -> 5, "f" -> 6}} *)

You can now convert this into the structure you desire. One of the several ways to do it is the following:

res = jsonLst // Nest[Map, Apply[List], 2];
(* {{{"a", 1}, {"b", 2}}, {{"c", 3}, {"d", 4}}, {{"e", 5}, {"f", 6}}} *)

EDIT

Following the suggestion by Mr. Wizard, this is indeed more general:

res = jsonLst // ReplaceAll[Rule -> List]

My intention was to actually give a more restricted solution so as to avoid unintended side-effects.

EDIT 2

And following the suggestion by b3m2a1, here is his recommended solution:

res = jsonLst // Replace[#, Rule -> List, {3}, Heads -> True] &

Your root JSON is an Array, so first create a JSONArray from your String.

Do this:

JSONArray arr = new JSONArray(jstring);
for (int i = 0; i < arr.length(); i++) { // Walk through the Array.
    JSONObject obj = arr.getJSONObject(i);
    JSONArray arr2 = obj.getJSONArray("fileName");
    // Do whatever.
}

For more info, please refer to the docs on JSONArray and JSONObject.

you can get this data as a JsonArray

Call getJSONObject() instead of getString(). That will give you a handle on the JSON object in the array and then you can get the property off of the object from there.

For example, to get the property "value" from a List<SomeClass> where SomeClass has a String getValue() and setValue(String value):

JSONObject obj = new JSONObject();
List<SomeClass> sList = new ArrayList<SomeClass>();

SomeClass obj1 = new SomeClass();
obj1.setValue("val1");
sList.add(obj1);

SomeClass obj2 = new SomeClass();
obj2.setValue("val2");
sList.add(obj2);

obj.put("list", sList);

JSONArray jArray = obj.getJSONArray("list");
for(int ii=0; ii < jArray.length(); ii++)
  System.out.println(jArray.getJSONObject(ii).getString("value"));