Firstly let me say that this is not a film about gnomes. It is arty and in French and about a young woman called Amélie who likes to change people’s lives. You might call it interfering but her motives generally seem to be good. When she was small her mother was killed by a suicidal falling Canadian tourist. When her father retired she encouraged him to travel which he (and her mother) had always wanted to do but thought they were not able to since they believed there was a problem with Amélie’s heart (which there wasn’t). Her father gets a gnome which he is very proud of. Amelie steals the gnome and gives it to her air hostess friend asking her to post pictures of the gnome from various exotic locations such as Cambodia, Russia, America, Greece and a couple I don’t recognise (see picture below and if you do please let me know). The gnome is returned later and presumably the ploy worked because towards the film the father is seen taking a taxi to the international airport.
The film was released in 2001 so it definitely did not start the traveling or roaming gnome phenomenon. It might, however have made the prank more popular and possibly influenced the Travelocity advertising campaign on the subject.