Francis Baxter attended high school in Dover, Oklahoma, where he played basketball and baseball.  His class had only 13 students.  He lettered in track and tennis at Central State University, where he graduated with a degree in Mathematics in 1956.  He was certified to teach 7th-12th grades.  He began teaching math and coaching tennis at John Marshall High School in 1956 and in 1960 moved to Harding High School where his boysí tennis teams won three Oklahoma State titles.  While at Harding, he helped administer the All-State Games.  In 1970, Francis began his career at Central State University.  He received his Masterís Degree in Teaching from Central State and began working toward a PhD from OSU.

Francis was the head coach of the Central State/University of Central Oklahoma Menís tennis teams for 36 years and of the Womenís tennis teams for 26 years before retiring in 2006.  He led the Menís and Womenís teams to six NAIA District 9 championships in the 1980s while taking the Men to three NAIA national tournaments and the Women to one.  He also guided his teams to eight combined NCAA Division II national tournament appearances, six for the Men and two for the Women.  In 1988 he was named the Lone Star Conference Womenís Coach of the Year and in 2004 the Lone Star Conference Menís Coach of the Year.  He also claimed the Division II Menís Coach of the Year accolades in 1996. 

Coach Baxter had 14 players earn NAIA or Division II All-American honors a combined 25 times, including Charl Bornman, the schoolís first-ever Division II National Champion.  He was the driving force behind UCO hosting the NCAA Division II National Tournament in 1991, 1992, 1993, and 1996 in addition to the ITA/Rolex National Small College championships in 1993 and 1994.

Francis was the Executive Secretary of the Oklahoma District Tennis Association for 32 years and was the Missouri Valley President from 1973-1974.  As a player, Baxter served as captain of a United States International tennis team from 1993-2001, leading the 60-and-over men to the Von Cramm Cup title seven consecutive years from 1993-1999 and taking the 50-and-over men to the Fred Perry Cup Crown in 2000 and 2001.  In 1999 he became the first Chair of the newly established Oklahoma Tennis Hall of Fame committee and is one of the five original inductees into the Oklahoma Tennis Hall of Fame.  He was inducted into the University of Central Oklahoma Athletic Hall of Fame in 1991 and into the Missouri Valley Tennis Hall of Fame in 2009.  Because of his success at Harding High School, Coach Baxter was inducted into the Oklahoma High School Tennis Coaches Hall of Fame in 2016.  In 2017, Baxter was inducted into the prestigious Intercollegiate Tennis Association Hall of Fame in the same class as James Blake and Nick Bolletieri. 

Francis and his wife Jean live in Edmond, Oklahoma.  In 1980 they became charter members of Faith Bible Church where he was an elder for 9 years and Junior High Sunday School teacher for 15 years.  In 2021 Coach Baxter will be honored for life-time contributions to tennis and UCO with the erection of a life-size bronze statue at Edmondís new Center Court public tennis facility.  The Baxter statue is being funded with private donations through the Oklahoma Tennis Foundation and the Edmond Visual Arts Commission.  Francis passed away September 9, 2021.