She was Margaret Ann at both her marriage registrations.

The only birth record found has been the censuses:

In 1841 she was born in 1823 in Co Durham,
In 1851 she was born in 1821 in Stockton, Co Durham,
In 1861 she was born in 1823 in Durham, Co Durham,
In 1871 she was born in 1822 in Stockton, Co. Durham,
In 1881 she was born in 1821 in Stockton on Tees, Co Durham,
In 1882, at death, she was born in 1818.

Take your pick?  I have picked 1823 as that was given by her parents and they should have known.
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In 1851 they were living at Ryhope Mill, Sunderland, Durham with 3 sons and 1 dau:

First name(s)  Last name  Relationship  Marital status  Sex  Age  Birth year  Occupation  Birth place
Luke      Trewhitt Head     Married    Male    30  1821  Miller  Bishopwearmouth, Durham
Margaret  Trewhitt Wife     Married    Female  30  1821  -       Stockton, Durham
Francis   Trewhitt Son      -          Male     4  1847  -       Ryhope, Durham
Edward    Trewhitt Son      -          Male     3  1848  -       Ryhope, Durham
Isabela   Trewhitt Daughter -          Female   2  1849  -       Ryhope, Durham
Luke      Trewhitt Son      -          Male     0  1851  -       Ryhope, Durham
Ann       Dixon      Servant  Unmarried  Female  21  1830  House Serv   Durham

Ref:
Archive reference  HO107
Piece number       2396
Folio              533
Page               23
Combined:          HO107, piece 2398, folio 533, p. 23
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In 1861 she was widowed and they had moved to 24 Deptford Road, Bishopwearmouth, not far from her parents; her first son and first daughter were not at home:

First name(s)  Last name  Relationship  Marital status  Sex  Age  Birth year  Occupation  Birth place
Margaret   Trewhitt  Head      Widow  Female  38  1823  Formerly Victualler  Durham, Durham, England
Edward     Trewhitt  Son       -      Male    13  1848  Glass Maker Apprentice  Sunderland, Durham
Luke       Trewhitt  Son       -      Male    11  1850  Shipwright Apprentice  Bishopwearmouth, Durham
Ann        Trewhitt  Daughter  -      Female   9  1852  Scholar  Bishopwearmouth, Durham
George     Trewhitt  Son       -      Male     7  1854  Scholar  Bishopwearmouth, Durham
Mary Jane  Trewhitt  Daughter  -      Female   5  1856  Scholar  Bishopwearmouth, Durham

Ref:
Archive reference  RG09
Piece number       3769
Folio              37
Page               4
Combined:          RG09, piece 3769, folio 37, p. 4
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In 1871 she was in Ravensworth Street, Bishop Wearmouth, Sunderland, Durham with her new husband and two of her Trewhitt children:

First name(s)  Last name  Relationship  Marital status  Sex  Age  Birth year  Occupation  Birth place
Joseph      French  Head      -  Male    60  1811  Glass Cutter Unemployed  Shields, Co Durham
Margaret A  French  Wife      -  Female  49  1822  -                        Stockton, Co Durham
Luke T      French  Son       -  Male    20  1851  Joiners App              Ryhope, Co Durham
Mary J T    French  Daughter  -  Female  14  1857  -                        Ryhope, Co Durham

Ref:
Archive reference  RG10
Piece number       5001
Folio              48
Page               19
Combined:          RG10, piece 5001, folio 48, p. 19
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In 1881 her census details are a tad confusing; she was at 1, Chester Place, Bishop Wearmouth, Sunderland, Durham:

First name(s)  Last name  Relationship  Marital status  Sex  Age  Birth year  Occupation  Birth place
Margaret  French    Head        Married  Female  60  1821  -  Stockton on Tees, Durham
Luke      Trewhitt  Son In Law  Married  Male    30  1851  Joiner  Ryhope, Durham
Jane E    Trewhitt  Daughter    Married  Female  32  1849  -  Bishopwearmouth, Durham
Luke      Trewhitt  Nephew      Single   Male     9  1872  Scholar  Bishopwearmouth, Durham

Ref:
Archive reference  RG11
Piece number       4987
Folio              58
Page               110
Combined:          RG11, piece 4987, folio 58, p. 110

From the enumerator's sheet, the transcript was correct, though I think the first Luke Trewhitt was her son, Jane was her daughter-in-law and the seocond Luke Trewitt was her grandson.  I also supect that Margaret was by then a widow.

However Joseph was found in 1881 as a boarder with a family of Frenches, the eldest of whom was a glass cutter and probably his son.
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This has to be her death:

First name(s)  MARGARET ANN
Last name      FRENCH
Gender         Female
Birth year     1818
Age            64
Death quarter  1
Death year     1882
District       Sunderland
County         Durham
Volume         10A
Page           282
Country        England
Record set     England & Wales Deaths 1837-2007
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From the Durham County Advertiser of 27 February 1846:

"At Gateshead, at St Mary's Church, 18th inst, Mr Luke Trewitt, miller, to Miss Margaret Ferrand."
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Their marriage index:

First name(s)     MARGARET ANN
Last name         FERRAND
Marriage quarter  1
Marriage year     1846
MarriageFinder  MARGARET ANN FERRAND married one of these people
                Jacob Reuter, Jacob Renter, Robert Fulthorp, Luke Trewhill, Hugh O'neil
District        Gateshead
County          Durham
Country         England
Volume          24
Page number     114
Record set      England & Wales Marriages 1837-2005
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Their marriage index:

First name(s)    MARGARET ANN
Last name        TREWHITT
Marriage quarter 3
Marriage year    1862
MarriageFinder   MARGARET ANN TREWHITT married one of these people
                 Joseph French, Edward Hall
District         South Shields
County           Durham
Country          England
Volume           10A
Page number      596
Record set       England & Wales Marriages 1837-2005
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