Take my review with a grain of salt: I have read all of the books to date in the original French (up to the 4th: "Arthur et la guerre des deux mondes"), so I can comment on the story and original writing, but it is possible the translation may have exacerbated any problems regarding use of language.
"Fun" is the most appropriate word for this work. Originality is unfortunately lacking to some degree. The premise of "Honey I shrunk the kids" + some character elements from "Harry Potter" = "Arthur and the Minimoys"
Even in French, Besson is a somewhat sloppy writer, relying too heavily on almost infantine similes. I am assuming these only worsen in translation.
I did however enjoy the characters. There is something typically French about the relationships of the personages that makes this book worth plugging through, which further matures in the 2nd installment. I would recommend this book just to get to the sequel.
To help you decide whether or not this is worth your time investment, I've included a note about the following books (no spoilers included)
"Arthur et la Cite Interdite" - 4 stars
The character development is heart-warming. This book really shines and creates a genuine desire to read more.
"Arthur et la vengeance de Maltazard" - 2 stars
Terrible. 75% of this book is flashbacks to help you better understand the characters. Almost no action is involved. I felt like it would never end. It could have worked if the stories told about each character related to what was currently happening (or not happening!) in the plot, but things almost tie together near the end.
"Arthur et la guerre des deux mondes" - 2 stars
Boring. Besson decides to come back to the actual hear-and-now, but the events really aren't that interesting. This could have been a platform to further explore the relationships between the characters, but of this opportunity Besson never takes advantage. I was expecting some interesting, almost cataclysmic event (the title translates to "Arthur and the war of the two worlds"), but even this is dissappointing.
Unless more sequels of note are released, I would suggest reading the first two books and stopping.