"Genevieve" a common 19th century name?

[Maiden Stone]

“Jennie” sounds like a logical pet name for Genevieve I would say.  Sweeping statement ... I don’t think Jennie would be a common pet form of Jane.  Jeanne is a French form of Jane, perhaps this could sound similar to Jennie depending how you say it?  You might find a loose connection that way? There are no rules though. 

My English Janes, born 18thC were all known as Jinny on some documents. One was Ginney in burial register.

[Ruskie]

That is interesting MS. Maybe a family fashion. 

One of my OH’s families had 10 children and most of them had seemingly illogical pet names which bore no resemblance to their given names. Eg Robert, known as ”Peter” ... Beatrice, known as “Mid” ... (though I was told the reason for this one).

[Maiden Stone]

I had never thought about the French connection to this name.  That's interesting.

Genevieve was patron saint of Paris because she was twice credited with saving it from attack in the 5th century. One of the invading forces was the Huns
Paris was besieged 1870-71 by the Prussians during Franco-Prussian War. A French leader escaped by balloon. (Prussians were German. The German army in WW1 was called "the Hun" by their opponents.)
 Defeat by Prussia ended the Third Empire. The Empress and her son, the Prince Imperial went to live in England. Britain and France were allies at the time. Queen Victoria had cordial relations with the Emperor and Empress. The Prince Imperial died young and the Prince of Wales (Victoria's eldest son & heir) was chief mourner at his funeral. (A cousin of my 2xGGF did the music.)
Some families in Britain and perhaps elsewhere around this time named children after contemporary heroes and heroines and other people they admired and characters from myth and literature. Guiseppe Garibaldi, Italian nationalist leader had British namesakes; Florence became a girl's name as did Shirley, instead of male names as previously. Genevieve may have been another such name, gaining popularity, in honour of the French saint and in sympathy with the French people. (This is only my theory.) From what I saw of Irish bearers of the name Genevieve, many seemed to have been educated city-dwellers, the sort of people who had leisure to read.
Parents have been known to name children after unrelated people whom they might have regarded as benefactors, or hoped they might become so.
My 4xG grandparent had 8 sons and ran out of family names by number 5. After searching fruitlessly for ancestral namesake of my 3xGGF, son no.7, I realised, upon discovering his Catholic baptism register that he was called after his godfather, who later married the baby's cousin. Son no. 6 was named for his step-grandfather (I didn't know he had one) and no. 8 for a member of the family of the lord of the manor.
Another of my families had 6 girls in a row; 5 were family names but I don't know where my 3xGGM's name came from.

[Maiden Stone]

That is interesting MS. Maybe a family fashion. 

It seemed to be common in Lancashire. They were also Jen(n)et. 2 were mother-in-law and daughter-in-law. The other was granddaughter of the daughter-in-law. The daughter-in-law was married as Jenet and buried 62 years later as Ginny, aged 86, widow of her second husband. Another old woman belonging to her 2nd husband's family was also Ginny in same burial register 6 years earlier. The "G" spelling was less common. The granddaughter was Jinny in C. of E. baptism register and Jane in C. of E. marriage register. I think she was Jane or Joanna (maybe both at different times) in Catholic baptism and marriage registers.

[Ruskie]

It is interesting how people select names for their children.

I have told this story before, but I found a piece written by the father of one of the families I was researching in which he helpfully explained how he decided on the names for his children. It is quite enlightening - my favourite was a middle name given to his daughter ‘in honour’ of someone who was “kind” to his wife. With common names it can be more difficult to work out who the child is named after, if anyone, even if they follow a Scottish or Irish naming pattern for example. You might find both fathers are William, as was an older decesaed sibling, and an uncle or two, a cousin, a neigbour and an employer.