As has already been stated, you have an identification tag from the following individual:
Name: William Gamelin
Unit: Company L, 57th Infantry
Soldiers in the US Army were assigned serial numbers around 28 February 1918. The fact that this tag does not have a serial number indicates that it was probably issued prior to that date. The attached card from the U.S. Veterans Administration is probably for your soldier.
Date of Birth: 11 May 1889
Residence: 369 Dubuque Street, Manchester, New Hampshire
Date of Enlistment: 25 May 1917
Date of Discharge: 29 July 1919
Rank at Discharge: Private 1st Class
Unit at Discharge: Company A, 13th Machine Gun Battalion (5th Division)
Army Serial Number: 1,197,297
Date of Death: 21 October 1944
The serial number 1,197,297 was part of a block of serial numbers (1,000,000 to 1,200,000) issued to soldiers serving in the Southern Department,Fort Sam Houston, Texas, in February 1918. This fits with William Gamelin having been assigned to the 57th Infantry at that time. The 57th Infantry served at the following locations during the war:
Organized at Camp Wilson, Texas, in June 1917
Sent to Camp Funston, Kansas, in July 1917
Sent to San Benito, Texas, in October 1917
Sent to Brownsville, Texas, in November 1917
Sent to Houston, Texas, in December 1917
Sent to Camp Logan, Texas, in May 1918
Sent to Camp Pike, Arkansas, in December 1918
Sent to Camp Dix, New Jersey, in November 1919.
As indicated above, the 57th Infantry did not serve in France during the war. Gamelin was most likely transferred from the 57th Infantry to the 13th Machine Gun Battalion as a replacement. The 13th Machine Gun Battalion was also stationed at Fort Sam Houston from November 1917 to March 1918. A forum member with access to Ancestry.com or Fold3 should be able to identify the exact unit he sailed to France with.
The tag in your possession was most likely discarded when Gamelin was issued a new set of tags that had been stamped with his updated service information (probably just his name, serial number, and USA). He was no longer a member of the 57th Infantry at that time, so there would have been no reason for him to keep it. The blank tag you found with it was probably given to Gamelin but never stamped. All U.S. soldiers were supposed have two idenfication tags, but errors (men being sent over with old tags showing incorrect units or blank tags) continued to happen even late in the war.