It appears from the data on John's brother Jennings Bryan Petit that these are the parents.
Source: "United States Census, 1900," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MSD3-XGX : accessed 27 February 2017), John T Petit in household of Francis Petit, Civil District 12, White Pine Tree, Jefferson, Tennessee, United States; citing enumeration district (ED) 53, sheet 14B, family 268, NARA microfilm publication T623 (Washington, D.C.: National Archives and Records Administration, 1972.); FHL microfilm 1,241,580.
United States Census, 1900 Civil District 12, White Pine Tree, Jefferson, Tennessee
Francis Petit Head M 38 North Carolina
Lydia M Petit Wife F 41 North Carolina
Kettie L Petit Dau F 14 North Carolina
William H Petit Son M 13 North Carolina
John T Petit Son M 10 North Carolina
James M Petit Son M 8 North Carolina
Garland A Petit Son M 6 North Carolina
Jennig B Petit Son M 3 North Carolina
Margret E Petit Mother F 63 North Carolina
Source: "North Carolina Deaths, 1931-1994," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:FPQW-86Y : 1 July 2015), Jennings Bryan Pettit Sr., 16 May 1973; citing Asheville, Buncombe Co., North Carolina, 16678, State Department of Archives and History, Raleigh; FHL microfilm 1,983,768.
Name Jennings Bryan Pettit Sr.
Death 16 May 1973 Asheville, Buncombe Co., North Carolina
Burial Date 18 May 1973
Burial Place Brevard, N.C.
Residence 105 Minor Street, Brevard, Transylvania Co., North Carolina
White Male Age 76 Married
Occupation Shoe Repair
Birth Date 25 Jan 1897 North Carolina
Father Francis M. Pettit
Mother Lydia Galloway
Spouse Lottie Norton
Reference ID 16678