You might have noticed this if you've been studying 19th century French Popular fiction and the French WNU.
Since real life history doesn't seem to mention much happening in France in 1838 at all. I figure this is likely to have happened from later authors homageing the first who probably picked that year at random.
It begins with Eugene Sue who effectively founded several new genres when he wrote The Mysteries of Paris, originally serialized in 1842-43. It's events are all set in 1838.
Alexandre Dumas' The Count of Monte-Cristo was a project that began when he was prompted by his publisher to write something to copy the success of Sue's Mysteries of Paris. While the Novel's story spans from 1815-1844, the bulk of the main narrative, Dantes actually carrying out his revenge plan, pretty much everything that the Anime Gankutsuou adapts, is set in 1838, (as well as all the scenes featuring Eugenie Danglers and Louis d'Armilly). So pretty much everything people actually want to see.
Much later Paul Feval would write his Blackcoats saga. The second half of Salem Street and the entirety of The Invisible Weapon, is set in 1838.
In the introduction for his translation of The Invisible Weapon, Brian Stableford talks about how that novel is perhaps the most Suesque of Feval's novels, echoing many things Sue did but also doing them very differently. Most of the parallels he mentions are to The Wandering Jew besides that it features a character locked up in the same Paris prison as The Mysteries of Paris. But I think that it's being set the same year as the Mysteries of Paris is not likely to be a coincidence.
Spoiler for The Blacckoats novels ahead
Especially since setting those events in that year caused one of the major continuity hiccups of the saga. What we're told about Saladin in the original novel and Heart of Steel (written before) and The Companions of The Treasure (written after) place Saladin's birth in 1840, this novel alone contradicts that by featuring him in 1838.
There's no major reason you couldn't move the events of the novel up two or three years to fix that issue. But it'd still be a problem that it effectively depicts the break up of Echolat and Simolor before we ever meet them in the original novel. And makes one wonder why Maman Leo is completely absent for their story-lines in the events set in 1842 and early 43 in the first two novels.
Sue's second major novel was set in 1832, that year was also of interest to later writers. But it was more real life historically significant due to the June Rebellion (fictionalized in Les Miserables by Victor Hugo) and other lingering aftermaths of the July Revolution. And Dumas's novel dealing with that year (She-Wolves of Machecoul; The Last Vendée) was also based on real history of that year, and for Feval's secret history it's only the extended prologue of Heart of Steel, Marguerite's origin story, that is set during 1832, and is early in the year during Lent.