According to the New England Families Genealogical and Memorial: Third Series, Volume IV:  "Of his ancestry or birthplace (Thomas) no positive evidence has been found. According to Bishop Henry Bidleman Bascom, one of his descendants, the family was French." 

The Online Bascom Genealogy site says that: "... although definitive proof has not been established, we believe Thomas can be traced back to the earliest known French Bascoms of the 1400's."  The book "Bascom and Allied Families", by Mrs. Joseph Dayton Bascom, (1932) covers the French and English Bascom lineage according to Brad Bascom, the President of the Bascom Reunion Association.  "While some source material and validation is lacking it is currently the only source we have on this lineage."

The first 7 generations as presented by this site are as follows:

01. Gilbert Bascom - married Jehanne De Mons
02. Guillaume Bascom (1410-1490) married Marie De La Croix
03. Guillaume Bascom (1443-1511) married Adelaide De Chabanne
04. Jean Bascom (1470-1562) married Suzanne Barbey
05. Robert Bascom (1499-) married Marie Dornant
06. Jean Bascom (-1617) married Margaret Barber
07. Jean Bascom (1570-1625) married Jane Beaumont

08. Thomas Bascom ^[1] was born abt. 1604 in Fordington, Dorsetshire, England.  He emigrated from England around 1634 in the Mary and John." He settled first in Dorchester, MA among the other settlers of this ship. In 1689 he moved to Windsor, CT, and in 1655 settled in Northampton, MA where he was among the first settlers of that town. Soon after he arrived Thomas was appointed commissioner to end small causes and is later referred to often in the Northampton town records as "Constable Bascom". He married a woman with the Christian name Avis.  He died on May 9, 1682.

The children of Thomas and Avis are:
 

1	Hannah Bascom (Born before 1640 -)                                 Married (1) John Broughton on Nov 15, 1650                                 Married (2) William Janes on Nov 20, 1642
2	Abigail Bascom (See Below)
3	Thomas Bascom (Born on Feb 20, 1641/2 in Windsor, CT - Died                                  on Sep 11, 1689 in Northampton, MA)                                  Married Mary Newell on Mar 20, 1666/7
4	Hepzibah Bascom (Born on Apr 14, 1644 in Windsor, CT - Died                                    Sep 20, 1690 in Northampton, MA)                                    Married Robert Lyman on Nov 5, 1662
5	Unknown Bascom (Died in 1647 in Windsor, CT)

 

09. Abigail Bascom ^[1] was born on June 27, 1640 in Windsor, CT.  She married John Ingersoll, son of Thomas Ingersoll and Margery Eaton on Dec 12, 1657 in MA.  Abigail died in April, 1668 in Westfield, Hampden, MA.  I descend from their daughter Hester Ingersoll who married Benoni Jones. 

LDS records and Online Bascom Genealogy list the ancestors of Thomas Bascom back to Gilbert Bascom, who was born in the late 1300's and married Jehanne De Mons.