I feel me stupid...
How to understand that "The form already has an attachment control" " but "I noticed that the file attachment control is not showing"?
Just drag&drop the Attachments from Fields pane onto your design surface of a form in Infopath Designer 2010 (or choose the desired place in form and right-click on Attachments > . If you do not see Fields side pane, then under Data tab on ribbon, click Show Fields button
If you do not see Attachments in Fields, make sure that Attachments checked as Enabled in Advanced Settings of List (or Library, or what? you did not write what) by navigating to (what?) and under List (or Library or what?) tab on ribbon, press (Library/List/what?) settings