"I want to find out more on Arch and Jennie and their offspring" Do you mean their siblings and parents ? Was Jennie nickname for Virginia ?

Frances - female
Francis - male

Known children of Carlos Elton Arnold and Mary Frances/Francis Smith:
James Elton 29 Jul 45 Frio County
Barrett Anthony 7 Dec 56 Bexar County

James E Arnold born July 1945 known to have lived in Harlingen.

Barrett Anthony Arnold Jr born 13 Oct 1980 Bexar County, father listed as Carlos Elton Arnold, no mother's name.

James Elton Arnold & Joy Beth Nelson: Mary Elizabeth 15 Jan 1987 Hunt County

Carlos Elton must have had a brother named George Barrett Arnold who had two children in Frio County with Rebecca Josephine Gillis or Jillis; Jack T 5 Dec 41 and Brenda Jo 10 May 44.

Barrett A Arnold married Denise C Loest b abt 1961; 24 Feb 1980 Bexar County, divorced 14 Jul 1983 Bexar, 1 child

Barrett A Arnold married Linda F Steven b abt 1948; 30 Aug 1984 Travis County and known to live in San Antonio area.

MARY FRANC ARNOLD
20 Dec 1916 - 17 Apr 1983
last residence 78061 Pearsall, Frio, TX) (none specified)
Death County: Frio

Arnold, Mary Frances 17-Apr-1983 Frio

1930; Census Place: Precinct 3, Tarrant, Texas; Roll: 2398; Page: 10A; Enumeration District: 115; Image: 1031.0.
Arch Smith 57 born about 1873 in Arkansas
Jeannie Smith 52 abt 1878
Hugh Smith 21 abt 1909
Ruth Smith 16 abt 1914
Francis Smith 13 abt 1917

1920;Census Place: Arlington Heights, Tarrant, Texas; Roll: T625_1848; Page: 2B; Enumeration District: 87; Image: 215.
Aarch Smith 44 1876 AR parents AR
Gennie Smith 49 1871 VA parents VA
Hugh Smith 10 1910 TX
Ruth Smith 7 1913 TX
Francis Smith 3 1917 TX

26 April 1910; Census Place: Fort Worth Ward 13, Tarrant, Texas; Roll: T624_1591; Page: 10A; Enumeration District: 155; Image: 591. - Mansfield Road
Arch Smith age 34 born Arkansas 1876, married 6 years, father/mother AR, farmer
Jennie Smith age 30 born Virginia 1880 father/mother VA, had 3 children, 1 living
Hugh Smith age 1 and 7 mos 1908 TX

Name: Arch Smith
Death Date: 22 Jun 1944
Death County: Tarrant
Certificate: 30233

Name: Arch Smith
Death Date: 19 Apr 1968
Death County: Tarrant
Gender: Male
Marital Status: Widowed

Name: Jennie Smith
Death Date: 9 May 1964
Death County: Tarrant
Gender: Female
Marital Status: Widowed

Jennie Smith 4 Aug 1964 Bexar County widowed
Jennie Smith 1 Oct 1964 Ector County widowed

Infant of Arch Smith born 2 Mar 1907 Tarrant
Infant of Arch Smith born 23 Nov 1908 Tarrant
Infant of Arch Smith born 20 Dec 1916 Tarrant

HUGH J Smith 23 Nov 1908 - 30 May 1992 (not specified) (none specified) 458-54-3445 Texas

Name: Hugh Smith
Death Date: 30 May 1992
Death County: Tarrant
Gender: Male

?
children of Hugh Jefferson Smith & Edith Oleta Daniel or Oleta Eva Daniel:
Horace Hugh 19 Dec 35 Tarrant
Jerry Dean 25 Jan 38 Tarrant

Horace H Smith born Dec 1935 found public records in Grapevine

Jerry D Smith born Jan 38 found public records in Tyler Texas
Jerry D Smith born Jan 38 found public records in Houston, same person, wife named Ann A born abt 1942

?
Name: Jennie Foster
Home in 1900: Walton, Charlotte, Virginia
Age: 21
Estimated Birth Year: abt 1879
Birthplace: Virginia
Relationship to head-of-house: Daughter
Father's Name: Josie T 1841 VA
Mother's Name: Virginia A 1851 VA
Race: White
Washington Foster 1881 VA son
Sampson Foster 1884 VA son
Jelckey Foster 1891 VA dtr
Dorcas Foster 1893 VA dtr

http://www.familysearch.org
Jennie (Seba V) Foster
Jan 1879 VA
Father: Josiah Thomas (Joseph) Foster
Mother: Virginia Alice Wallace

Archibald G Smith aka Arch Smith
July 1877 or 1878 Washington AR
Father Robert C Smith
Mother Jane

Robert C. SMITH Self M Male W 57 OH Farmer OH OH
Jane Smith Wife M Female W 44 VA Keeping House VA VA
Ira N. SMITH Son S Male W 17 IL Works On Farm OH VA
Uriah Smith Son S Male W 11 OH OH VA
Perry Smith Son S Male W 9 KY OH VA
Flora E. SMITH Dau S Female W 6 VA OH VA
Archibald G. SMITH Son S Male W 2 AR OH VA
George FERRELL SonL M Male W 35 TN Farmer VA VA
Susan M. FERRELL Dau M Female W 19 IL TN VA
Robert S. FERRELL GSon S Male W 1M TN Ar IL ---
--------------------------------------------------------------------------------
Source Information:
Census Place Mars Hill, Washington, Arkansas
Family History Library Film 1254058
NA Film Number T9-0058
Page Number 510B

1900; Census Place: West Fork, Washington, Arkansas; Roll: T623 79; Page: 10A; Enumeration District: 118.
Jane Smith age 63 born April 1837 West Virginia, widow, bore 7 children, 5 living, father NC, mother WVa
Arch Smith age 22 born July 1877 AR father Ohio
Perry Smith age 29 born May 1871 KY married 1 yrs
Flora Smith age 29 born Apr 1871 AR wife of Perry

Happy Hunting !