RouxRC, your reply is obviously wrong !
“adresse data gouv fr download” indicates the same “Licence Ouverte - Open Licence” (LO-OL) for the two datasets that make up the BAN.
So RouxRC, visibly you’ve confused BAN and BANO (BAN is slow to update). But even if these two datasets have different licences (LO-OL for the two datasets of the BAN, and ODbL for the BANO), BOTH are open licences.
BANO is a separate project maintained by OpenStreetMap France, that developed separately, by requalifying data from the BAN (notably adding richer addresses without abbreviations or capitals everywhere, and with normal accents), and integrating it as well to the rest of the geodata and with many quality tests. So BANO is more precise and more verified than BAN which contains numerous errors.
BANO was started by OSM France exactly because the situation of the BAN was very bad. But an agreement was finally made between BAN and BANO, and now OSM France is an official partner and contributor to the BAN (whose legal situation for licencing was also clarified: LaPoste and IGN are no longer blocking this, and the official status of LaPoste and IGN themselves have largely changed because of the European requirements and the need to open the competition: most old monopoles of national egencies are now over, except in a few areas related to national security and exceptions covered by privacy and regulated by “Loi Informatique et Liberté” since 1976, when France was among the first countries to propose a legal protection of privacy, and regulated by French CNIL, which can now also take financial sanctions and act directly in justice: CNIL is no longer giveing advices, it can give orders and acts in France as one of the regulators approved by the European Union).
Anyway BANO (OpenStreetMap France) is one of the contributors to the BAN. But the BAN is very long to synchronize and aggregate its sources (notably, the contribution by LaPoste which continues using some private/unpublished data, and still has lot of errors that take years for them to fix; visibly LaPoste is the worst contributor to the BAN, while IGN and the Cadastre (Etalab and French minitry of Economy) is much more responsive and reacts to signalments made in OSM: there’s a real convergence between OSM and the Cadastre. And the situation between OSM and IGN has also largely improved and continues to improve (even the IGN now integrates OSM data it its proposed data layers and vizualisations, and it even generates its own OSM-based base maps and its own tile servers). OSM is now also a key provider in EtaLab’s data(dot)gouv(dot)fr, just like other national or local public agencies.
Note also that postal codes (“zipcodes” is the wrong term) were maintained in the past exclusively by LaPoste, but it lost all its monopole on postal services. Now this is the competence of a regulator, ARCEP (Autorité de régulation des communications électroniques et des Postes) and by law, postal codes are commons and must be freely usable by all competitors, and there’s a legal right for every resident in France to have an address without asking for permission. Street names and toponymy has never been in the competence of LaPoste but of municipalities (communes). Only the name of communes and official collectivities is regulated nationally (must be approved by prefectures acting under the Ministry of Intérieur only by delegation and not by transfers, or nationally by the Parliament).
The communes (not LaPoste) are also assigning the house numbers in the street, and they (or the EPCI to which they belong and where they delegated this role) are recorded in the Cadastre that they maintain locally for the Ministry of Economy: the cadastre is open to any one (except the land ownership which is kept private and protected by law, for privacy reason when owners are individuals, or by the business secret when owners are organizations; but the limits or computed surface and the usability of land is public so we can know when it is built, if it contains environmental features to keep protected, including a single tree)
Really addresses in France are now open and the classification made for addresses and postcodes is wrong. both are open since years (it should have been the case since more than 15 years, but LaPoste abused its position as long as it had the monopole that it lost, and LaPoste was very longto transfer its data to ARCEP: people had to campaign to force ARCEP and the government to claim the data which is now openly used by all adminsitrations, commercial organizations, network managers, security agencies, and still LaPoste (which no longer can create its own postal codes without asking to ARCEP and publishing their use) but also all other postal competitors (not just in France but anywhere in the European Union or European Economic Area at least, and some other countries that have cooperation agreements with France or the European Union with comparable terms and adequate legislation to fairly protect these terms for access rights and reusability).
And “Open Licence - Licence Ouverte” is really open (its “two” names are just one combining English and French). You should better document about this licence which is approved as being open by almost all “open” rights promoters and organizations.