The movie's title in French is "Hors de prix" which means "overpriced, outrageously expensive" or "out of one's leagues, something one cannot afford or reach" rather that "priceless" (a priceless object would be one for which its value cannot be determined).
The 1 Euro coin used to symbolically open the door of the couple's future is inscribed with Leonardo da Vinci's Vitruvian Man which used to be the logo for a famous temporary employment agency, showing that Irène and Jean will manage financially.
Jacques boasts that he remembers Irene's name but it sounds like he actually calls her Helen (when he sees her again at the party) and he definitely calls her Emilia when sitting on the balcony.
As a nod to Cinderella, Irene loses her footwear and runs to her "prince".
Jean poses as the archduke of Edinburgh in order to help Irène. However, there is no archduke of Edinburgh, nor has there ever been. Only a duke of Edinburgh existed. The last duke of Edinburgh was Prince Charles. On his accession to the throne as Charles III, the title merged with the crown.