It is not, technically, a "coin". It's a medal.
As for the identity, I think we can help. Your pics are excellent for a first-try at zooming on on such a small object; I'm fairly sure our inability to read it fully is more a problem with the medal itself, rather than your ability to read or photograph it.
It appears to be commemorating the birth or christening of a child, named Henri. I can also read "DUC DE BORDEAUX" behind the child's head. From this, I can deduce that the child is
Henri, Duke of Bordeaux, who may or may not have been briefly and technically King Henri V of France. He was born in 1820, which is presumably something like the date of issue for your medal. The Wikipedia image of his father,
Charles, Duke of Berry, shows him wearing the same style of high-collared uniform as depicted on your medal.
Whether the jewellery mounting around the medal dates from the same time is uncertain. Given the political nature of the subject depicted, your piece may have been used as a badge indicating loyalty to the legitimist monarchist faction when Henri was making another bid for the throne, after the fall of the Second Empire.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis