I see from another of your posts that they were living in PEI.
This seems to fit for them.
1901PRINCE WEST, PRINCE EDWARD ISLAND
Francis, age33, farmer, born May 8, 1867 PEI
Emelie, age 33, wife, born June 9, 1867 PEI
Axela, age 6, daughter, born Aug. 27, 1894 PEI (name looks like Adela in image)
Evangeliste, age 4, daughter, bon Aug. 3, 1896 PEI
Louis, age 2,son , born May 11, 1898 PEI (may be 17th)
Marie, age 11/12,daughter, born May 18, 1900 PEI
all are shown as being French
next door to them in another Aucoin family so perhaps parents of Francis
Amable, age 68, farmer, born March10, 1832 PEI
Marguerite, wife, age 55, born July 6, 1845 PEI
Joseph, son age 30, farmer's son, born Aug. 29, 1870 PEI
Marie, daughter, age 27, born July 23, 1873 PEI
James, son, age 20, farmer's son, born May14, 1881 PEI
Sophia, daughter, age 14, born Dec. 25, 1886 PEI
I went to 1891 census to see if I could find Amable and Marguerite to see if they have a son Francois/Francis
I believe this is the right family AND son Frank matches with age for Francis in 1901 census.
LOT 6, PRINCE, PRINCE EDWARD ISLAND
Lernob, age 48, farmer
Maggie, age 38, wife
Frank, age 23, son, lumberman
Joseph, age 20, son, fisherman
Mary, age 16, daughter
Ferman, age 13, son
James, age 10, son
Sophia, age 4,daughter
the names above are as indexed, in the image Ferman is Filman, Lernob does look like that in the image ?
all are shown born PEI with both parents born PEI
I only found one Emelie Gaudin of right age in 1891 census
1891 LOT 1, PRINCE, PRINCE EDWARD ISLAND
Peter, age 82, shoemaker born NB father born Nova Scotia mother born Quebec
Adelle, age 60, wife, born Quebec parents both born Quebec
Antaine, age 28, son shoemaker (looks like Antoine in image)
Paul, age 23, son, shoemaker
Emile, age 24, daughter
all the children born PEI father born NB mother born Quebec
I went to the PEI online archives and there is a Francois Aucoin born APril 10, 1868 baptized May 30, 1868, son of Amable Aucoin and Marguerite Poirier
so this means either the fellow in 1901 is the right one OR he is not as the birthdate shown in the census does not agree BUT
I tend to think he is the right one and whoever gave the info to the census taker got it wrong which is quite common in census records.
With him living right next door to Amable and Marguerite it seems very likelyhe is their son and they dohave a son of right name and age in 1891 census.
At same site IU found some children of Francois Aucoin and Emilie Gaudain/Gaudin/Godain (the various spellings used)
Adoline Evangeliste born Aug. 3, 1896
Louis, born May 17, 1898
Marie Alvina born May 18, 1900
Francois Antoine born May 2, 1903
Catherine Angeline born March 23, 1905
Sophie Olive born Sept. 23, 1906
Emilie Bernadette born Oct. 3, 1908
Marguerite Helene, born March 17, 1911
Pierre Amable born Oct. 6, 1912
so missing is daughter Axela who is with them in 1901 census, but there is a Marguerite Adele Aucoin born Aug. 1, 1894 to Francosi Aucoin and Emelie Gaudet who I think is likely her. As you see some of the dates of birth for other children do not exactly agree with the census but again that is quite normal for census records.This would also make sense for her to be named Adele if that is in fact the name of Emelie's mother ??
There is no marriage database there though which is too bad as that may have helped to confirm the parent's names for Francois and Emilie
I can go further back in census if you would like.