Pas de Calais Archives:
http://www.archivespasdecalais.fr/Archives-en-ligneIs your family the one shown as in London in 1891 with Marie and Lucien as children, and in 1901 with Marie and a "M" (probably Maurice Belgaeul/Belghul on freebmd - born 1891, he sadly died in WWI as you can find here:
http://www.memoiredeshommes.sga.defense.gouv.fr/fr/arkotheque/client/mdh/base_morts_pour_la_france_premiere_guerre/ )
The 1882 marriage shows that Abel was resident at Saint-Aubin, born at Vaulx, his parents were resident at Vaulx and consented to the marriage, his future wife was resident in Saint-Josse as were her parents.
It appears in the 1886 census of Saint-Josse that Marie Belgoeul, aged 3, is living with her grandmother, Elise Macquet (women appear under maiden name in these records).
However, her birth is not found there. I checked Saint-Aubin, the residence of her father at his marriage, and sure enough she's there:
Saint-Aubin - 1830-1895, page 351.
However, brother Lucien is not.
http://www.geneaservice.com gave me a hint - he appears in later electoral rolls in France with his place of birth given as "Vicheux" - which doesn't seem to exist, but "Ficheux" does and there Lucien Edgar Belgoeul is registered in 1885, son of Abel Gaspard and his wife Alice-Elise Bellembert.
Marginal notes indicate that he passed away in Clichy-la-Garenne, 3rd Feb 1960.
Some information on Lucien's war service here:
http://ccsc.genealogie.free.fr/TH/fiches/Ind_00966.htm