Judging from this, Antoinette's grandfather was a supporter of the Jacobite claim to the English throne.
In the 'Glorious Revolution' of 1688-9, William of Orange, at the invitation of the English nobility, deposed James II, a Catholic. James went into exile in France in 1688; his supporters would drink to the king 'over the water'.
Charlie is Bonnie Prince Charlie, James's son, who tried unsuccessfully to claim the throne in 1745. He fled to France, disguised as a lady's maid, after the battle of Culloden, the final Jacobite rising.
Annette's family were possibly of Scottish Catholic heritage, hence their support for the Jacobites and, perhaps, their settlement in French Catholic Martinique rather than a British colony. Perhaps it also explains their relocation to the Caribbean: many supporters of the 1715 rebellion were deported to the British Caribbean.
Sir Walter Scott's Waverley, which was almost certainly on the Coulibri shelf, popularised and romanticised the Jacobite cause for his nineteenth-century readership.
Robert Burns wrote a poem called O'er the Water to Charlie.
Over the Water to Charlie is a Scottish and English folk song ...
...and Morris dance.
Click here to listen to an In Our Time on the Jacobite Rebellion.