Esperanto seems to do a lot of stuff with adverbs that other languages do not. The manner of the going to France, in this case, is "this-weekly." And not "weekly" in a present-habitual sense like we use it in English. But "weekly" as in there is some "week-ness" to the nature of the action. I think... :)
The "week" is describing when they will go. Thusly, it is technically an adverb. Esperanto dramatically improves one's understanding of technical grammar.
The second part makes sense. :) I was referencing the tips and notes for the -n ending though, they say:
"The -n ending is used when talking about the upcoming or past occurrence of a specific event:
Mi alvenos sabaton. = I will arrive (on) Saturday."
I thought in this case, the use of "this week" seemed similar.
It is a way of showing that the ĉi is associated with semajne but only with semajne. WIthout the hyphen it could (though only with difficulty in this sentence) be associated with another word. I sometimes think of this as "partial agglutination" as there are two words, but they aren't fully mashed together.
One of the authors of the Esperanto course (arguably "the" author) once messaged me privately to ask me to "correct" the spelling of ĉi which I had written (in a public message) without the hyphen. I agreed with him on this point (and still do, really) and "corrected" my mistake by adding the hyphen. In the meanwhile, I found out that not everybody agrees on this point. Jordan (Being Colloquial in Esperanto) writes a bit about that.
So to answer MikeSanMartin's question, no it doesn't change the meaning and there really isn't a purpose. However, you will often see ĉi written with a hyphen when used with an adverb other than a correlative.
The Duo software doesn't check for the hyphen.
There is a future progressive tense (“will be going”) in Esperanto and it's written using either 'estos X-anta' or 'X-antos', therefore “mi irantos” and “mi estos iranta” mean “I will be going” https://en.wikipedia.org/wiki/Esperanto_grammar#Compound_tense