SERRAVAL, France — As a European proposal to bolster digital privacy safeguards faces intense lobbying from Silicon Valley and other powerful groups in Brussels, an obscure but committed group has joined in the campaign to keep personal data flourishing online.

One of the European Union’s measures would grant Internet users a “right to be forgotten,” letting them delete damaging references to themselves in search engines, or drunken party photos from social networks. But a group of French archivists, the people whose job it is to keep society’s records, is asking: What about our collective right to keep a record even of some things that others might prefer to forget?

The archivists and their counteroffensive might seem out of step, as concern grows about American surveillance of Internet traffic around the world. But the archivists say the right to be forgotten, as it has become known, could complicate the collection and digitization of mundane public documents — birth reports, death notices, real estate transactions and the like — that form a first draft of history....