Per Booth's records:
Armstrong, Frank C., Col. F. and S. 3rd La. Infty. En. _. Roll for May and June, 1862, "Present. Apptd. Col. May 10th, 1862, Having Been Re-elected at Reorganization of the Regiment." Rolls from July, 1862, to Oct., 1862, "Absent. Assigned to Duty July 6th, 1862, as Acting Brig. Gen. of Cavalry for Army of West. Spec. Order 102 from Hd. Qrs. Dept. No. 2."

Per Guide to La Units (Bergeron):
It looks like Armstrong was promoted directly to Col rank. He does not show up as part of the command staff (LC or Maj) prior to his promotion/election or as a Company Commander.

I believe there are a couple of web sites with information on the 3rd La Infantry, perhaps they might be able to give a better answer

JIMT