Bancroft was born on November 25, 1839 in New Ipswich, New Hampshire to James Bancroft and Sarah Kimball. At an early age he was cared for by Mr. and Mrs. Patch of Ashby, Massachusetts, the neighboring town. While not legally adopted, they named him Cecil Franklin Patch Bancroft, adding Franklin Patch after the son Mr. and Mrs. Patch had who recently died. He attended public schools in Ashby as well as the Appleton Academy in New Ipswich. He entered Dartmouth College in 1856 at the age of sixteen and graduated in 1860 near the top of his class.
