The only Paris maker beginning with H is Housel but no mark like that anywhere.
The blochy multicolour background and gilding are most out of keeping for any European porcelain maker let alone those picky Parisians. The cherubs seem to be transfer printed.
Compare the quality of this to the Housel coffee can here (left)
http://www.antique-porcelain-online.com/paris-porcelain-coffee-cans.html
or indeed to any item of “porcelaine de Paris”.
No comparision. So I have to agree with TreasureHunterD.

Honestly, if I had to make an educated guess, as I have seen a great many French, Limoges etc. pieces of porcelain and especially trinket boxes. Based on the paint work and gilding and especially the dotted “i”, I would be willing to bet money that this is a fake that was made somewhere in Asia, probably mid 20th century or a little later. That’s only my educated guess but there is 20+ years of experience with these types of items behind that guess and I did take a pretty good look online and in my books and did not see that mark anywhere. On fakes, a lot of the time, the marks are made to look very similar to other legit marks so you get that feeling of having seen it somewhere before. Anyway, that is my thought.