Are abbreviations like HTH and similar ones

yes, there is a lot of abbreviations in french to use in messaging,

simple ones can be found either in french and in English as @paradise said,

for example, message become msg.

But here is a short list of abbreviations that we can use:

‘ne t’inquiète pas’: (this one is used when someone says thanks)

• firstly became : t’inquiète

• then : tkt (T’inKièTe)

‘à plus tard’:

• ‘à plus’

• ‘a+’

‘Salutations’ (i think it’s the base of this abbreviation)

• ‘Salut’

• ‘slt’

‘merci’

• ‘mrc’

Right now, i can’t think about complex abbs. with multiple words. They might be not very common.

here is a link covering this side of the french language, (but keep in mind that it might be outdated since language in generale tend to change)
Wikipedia

hope this helps