You want to 'undo' the git add that was done for a particular file.
Case 1: To remove a single file from the staging area use the following command:
git reset HEAD -- <file>
Case 2: To remove a whole directory (folder) from the staging area use the following command:
git reset HEAD -- <directoryName>
Note that Your modifications will be kept. Also, when you run git status the file will once again show up as modified but not yet staged.