combat, there is no chateau at St. Gilles mentioned in the action reports.
A little map:


Stalemate North of St-Lô (35th Division)
On 12 July the 137th Infantry resumed its attack on the stubborn enemy pocket near St-Gilles. (See Map 15.) The forward German strong-point, around the church, was still the job of the 1st Battalion. After a terrific artillery preparation, lasting 45 minutes and ending with a rolling barrage, the 1st Battalion drove through the church and the surrounding houses. Only three enemy prisoners were taken.
The 3d Battalion, bypassing the church strong-point and leaving it for the 1st to mop up, was aided by the end of resistance on that flank, but found plenty of opposition farther south and made small progress. The 2d Battalion fought most of 12 July around another enemy resistance center, a group of stone houses at la Petite Ferme,
MACHINE-GUN POSITION with abandoned German equipment in the sector where the 137th Infantry encountered such strong defenses. The firing slit through the hedgerow permits small traverse.
which changed hands several times during the day. This farmhouse proved as great an obstacle as the church at St-Gilles, and occupied the full energies of Companies E and F. Two tank destroyers had been attached to each battalion. They were not able to destroy the stubbornly-held enemy positions in the hedgerows; two of them became mired and another was disabled by a mortar burst. Late that evening Company G was committed on the left flank, but the day ended with the battalion still unable to advance after bloody fighting. On the left of the 35th Division front the 320th Infantry had made 200 to 300 yards advance in the day's fighting. (Hyperwar USA)
Salut