His remarks on Sunday were condemned by Jean-Marie Le Pen, the leader of the far-right National Front party and a presidential candidate, who said France had no reason to apologise.
Lang, a former education minister, had earlier met Abdelaziz Bouteflika, the Algerian president, and passed on a "message of friendship" from Royal.
He called for French schoolbooks to be revised to present a less "idyllic" account of colonialism.
Differences between Paris and Algiers over the impact of the colonial experience have prevented the signing of a peace and reconciliation treaty, with Algeria demanding apologies for crimes said to have been committed during the colonial era.
Le Pen, on French television, said: "If Mr Lang means ... the regrets we should have with respect to Algeria, that is a villainous opinion, it is scandalous to say that.
"If France has to ask for accounts, she should ask those who allowed the departure in ruin of a million French mainland people" after Algerian independence, Le Pen said.
Lang also called for the establishment of an international organisation of states bordering the Mediterranean, including Algeria, France, Italy and Spain and said if Royal were elected, France would pay more attention to the Mediterranean basin.