Francis M. Hayley's records are found under the name F. M. Haley

See:

F M. Haley

Residence was not listed;
Enlisted on 6/1/1862 as a Private.
On 6/1/1862 he mustered into "C" Co. AR 25th Infantry
(date and method of discharge not given)
(Estimated date of enlistment)

Sources used by Historical Data Systems, Inc.:
- Index to Compiled Confederate Military Service Records

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Also at the National Archives and Fold3

Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Arkansas