These days, there is quite a lot already indexed for France through various sites. Often my first stop if a proper location is not known is to look at GeoPatronyme and get a feel for how common the name is and where distributed.
Then Genealogie.com. This is a pay site, but with a little cleverness we can get it to give us quite a lot of info, then go look at the appropriate archives (e.g. Archives de la Vendée ).
In this case, I searched 'nom' as Cordier, 'prénom' as 'Pierre', and then on the results page, under 'Initiale du prénom' chose 'O' to pick up the 'Oscar'. Right away, up to the top of the list bubbles a Pierre Louis Oscar Cordier born sometime between 1825 and 1850 in La Roche-sur-Yon. Narrowing it down by going back to the search and putting in 'Cordier', plus a one-year range, shows this man was born 1842.
Instead of paying to see it on that site, we're going to go to the Vendée archives and try to pick it up on their free Etat civil database.
Unfortunately they don't make it easy to directly link, but a quick check of the index for 1842 (at the back of the births section, not right at the back) shows me he's there, number 192 (image 92 of 357).
His birth was registered 11 October 1842 - the son of Jean Baptiste Alexandre Cordier, aged 47, occupation something gendarmerie?, and Jeanne Pauline Mora.
in the case where a birth can't be found, tracking down a marriage in France is another way to find information on birth place and parents. His first marriage etc. can be tracked down as follows.
A popular American pay site, as well as geneanet.org, lead me to a possible marriage for him Ille-et-Vilaine. Using Geneanet gets me to the exact location - Rennes.
Rennes is one of the cases where the records are on the Municipal Archives site for the city. Judging by his age and the fact that he remarried in 1869, I went for the 1863-1872 Tables (ten-year indexes), which show the marriage was 21 Jan 1865, to Sainte Rousseau. To find the original - left hand side of page 8 on the 1865 marriages).
This shows this is definitely the same man b. 1842, with the same parents. He is, at this point, a tobacconist, and living in Hédé (now Hédé-Bazouges) although the marriage took place in Rennes. His parents, both who seem to be living, (father 'retired officer of the gendarmerie') were also living in Hédé. His wife's family were resident in Rennes.
(Obviously if we found the marriage first, we would then use this information to locate and double-check the birth record)
For my final trick, we can hop over to the Ille-et-Villaine archives:
'Etat civil' to find the possible death of his wife, but hidden under genealogy are 'recensements' - the census. Not often used in French genealogy because it's mostly unindexed, but Hédé was quite small - only 35 pages in the 1866.
On page 12 is this little bit of interest:
Louis Cordier, aged 23, tobacconist, listed with a group of seemingly unrelated people (a widow and her child, some older women), and then an 8-month old child, Adele Cordier.
Adele was b. Hede as 'Adele Louise Cordier', 1 December 1865, daughter of 'Louis Pierre', aged 23, tobacconist, and Sainte Rosseau. Sainte Rosseau, wife of Louis Cordier, died 13 December 1865, aged just 20.