Albertini, a business lawyer by profession, entered politics in 1995 as parliamentary assistant to Jean-Claude Étienne. Initially a member of the RPR, he became an elected official of the city of Reims in 2001 with Jean-Louis Schneiter.
In 2014, Albertini was second deputy to the mayor of Reims, Arnaud Robinet, in charge of security, events, good living, elections and worship. He retained this function for the re-election of the mayor in 2020 until his election in June 2022 to the mandate of deputy. The law on the non-accumulation of mandates prohibits a parliamentarian from being part of the executive of a local authority.