OK, this is too long for a comment, but isn't yet an answer. More documenting a search.
The Father-in-Law, Julien Paudois, actually lived (and died) in Lacordaire, Saskatchewan. His grave is on Find a Grave, and his probate records are in the Saskatchewan Probate Estate Files, 1887-1931 collection of Familysearch. (His middle-name was Pierre.)
This suggests that the card was filled out by someone who misheard (or mis-transcribed) what was said. This does not fill me with confidence about the birthplace actually being 'St.-Lagille'!
Julien Paudois Sr appears (with variant spellings of his name) in the Canadian census:
- Canada Census, 1901
- Canada, Northwest Provinces Census, 1906
- Canada Census, 1911
From which I found his wife, Josephine, and his son, also named Julien.
The search also led me to Julien (jr)'s immigration card:

Notice that his place of birth is given as being the same as Marie!
His son's name was given as 'John':

Anglicised from 'Jean' (see below). Julien (Jr) also (kind-of) anglicised his name to 'Jules' in the 1920 census.
I also found the record the christening of Julien (jr)'s child, Jean Jules Marie Joseph Paudois, on 9 July 1907 at Notre Dame de la Salette, Forget, Saskatchewan, Canada (in the collection Saskatchewan, Catholic Church Records, 1846-1957, also on Familysearch).
From that we also have his wife, Marie whose maiden name was Ménage.
The 1911 census gave her immigration year as 1904. (Julien Jr arrived in 1888).
I haven't yet found their Canadian immigration records (which might give a place of birth).
I followed their later lives in US Censuses of 1920, 1930 and 1940, but they just give birthplace as 'France'.
They weren't yet naturalised US citizens at the time of the 1920 census where Julien, Marie, and Jean identify as 'aliens' ('al' in the 13th column, just after the year of arrival, given as '1915'). [Note that the surname has been indexed as 'Pandors']

In 1930 they had moved to Oregon, and entered 1914 for the year of arrival, and 'na' for naturalised.
Ancestry has a record of a 'Julius Paudois' in Valley County, Montana in the Montana, County Naturalization Records, 1867-1970 collection. This is our man (a big THANK YOU to @JanMurphy for that!).
This gives us the date of birth for Julien Jr, as 26 May 1875, but place of birth is just given as France:

Marie/Mary's date of birth is confirmed as 1878, but the place of birth given is also just 'France'.
We also know from his deposition that Julius had been a naturalised citizen of Canada. Unfortunately, according to the website of the Library and Archives Canada:
Immigration, Refugees and Citizenship Canada holds records of naturalization and citizenship from 1854 to the present. The originals of records dated between 1854 and 1917 have been destroyed.
Apparently, the card index that survives 'rarely contains any other genealogical information', so is unlikely to help in our search.
There is also a 'Mary Paudois' in the collection Records of Aliens Pre-Examined in Canada, 1904-1954. (once again, a big THANK YOU to @JanMurphy!)
Even given the terrible image quality, it's clear that this doesn't give us any more useful information to help identify here place of birth.
However, if this is the right person, it seems she arrived in Montreal in July 1903.
Next steps:
- Try to locate Canadian immigration records &/or passenger lists for Marie Ménage (1903/1904), Julien & Josephine Paudois (1888), and Julien Paudois Jr (also 1888).
in the hope that they might specify their actual place (or places) of birth in France.
If anyone fancies checking the information above, that would be great.
Also, if anyone has any suggestions, feel free to chip in.
Like I said, very much a work in progress ...