Borne's two-day trip to the former French colony and major gas exporter comes after President Emmanuel Macron concluded his own three-day visit in August, following months of tensions.
In remarks during the forum's inauguration, Algerian Prime Minister Aimene Benabderrahmane called for "a sustainable dynamic" in trade with France based on "reciprocity and mutual interests."
Borne called for "a new dynamic of economic cooperation."
Before returning to Paris, she also met with President Abdelmajid Tebboune and said bilateral ties will continue with "regular visits and exchanges on the economic, political and technical levels."
Borne and her cohort are the latest in a string of top European officials to visit Algeria, Africa's top natural gas exporter, as officials seek alternatives to Russian energy supplies since the start of the war in Ukraine.
The European Union's energy commissioner, Kadri Simson, is also expected in Algiers on Monday and Tuesday.
But ahead of her trip, Borne's office said deliveries of natural gas to France were "not on the table."
Both Borne and Benabderrahmane stressed the need for Algeria to pursue economic diversification.
Benabderrahmane said Algeria must "end its dependence on natural gas and attract foreign investment" in agriculture, pharmaceutical and vaccine production, and renewable energy, which "offer positive prospects for French businesses."
The two-day business forum was organized by the Algerian Chamber of Commerce and Industry and Business France, a government agency promoting international investment, which brought representatives of some 70 French firms to the event.
Ties between the North African country and its former colonial ruler had deteriorated after Macron last year questioned Algeria's existence as a nation before the French occupation, and accused the government of fomenting "hatred towards France."
But the contentious subject of the two countries' history, particularly during the war, was not set to feature prominently on Borne's agenda.
Algiers and Paris maintain bilateral trade at a large scale, with France being the second largest investor in Algeria, according to the International Monetary Fund.