Her two-day trip along with 16 ministers — over a third of her government — comes just six weeks after President Emmanuel Macron concluded a three-day visit aimed at ending months of tensions with Algiers.
Borne is expected to sign deals on economic cooperation, including energy — although deliveries of natural gas to France are "not on the table," according to her office.
Ties between the North African country and its former colonial ruler had seen months of tensions after Macron last year questioned Algeria's existence as a nation before the French occupation, accusing the government of fomenting "hatred towards France."
But during his visit in August, Macron and his Algerian counterpart Abdelmadjid Tebboune drew a line under the spat, declaring a "new, irreversible dynamic of progress."
Borne is also set to meet Tebboune, as well as Algerian Prime Minister Aimene Benabderrahmane, with whom she is expected to sign several agreements.
In an interview with news website Tout Sur l'Algerie (TSA), she said the visit would focus on "education, culture, the ecological transition and the economy."
"More cooperation will be a source of growth for our two countries," she said.
Shortly after arriving, Borne will lay a wreath at a monument to martyrs of Algeria's eight-year war for independence, and visit a cemetery for French nationals who resided in Algeria during France's 132-year rule which ended in 1962.
But the contentious subject of the two countries' history, particularly during the war, will not feature prominently on her agenda.
During Macron's visit, the president had announced the creation of a joint commission of historians to examine the colonial period, including the war, but again ruled out a state apology for acts committed during the colonial period.
Borne's predecessor Jean Castex had been scheduled to visit Algeria in April last year but his visit was cancelled at the last minute amid tensions between the two sides.
Borne and her cohort are the latest in a string of top European officials to visit Algeria, Africa's top natural gas exporter, in search of alternatives to Russian energy supplies since the start of the war in Ukraine.
Algeria's Sonatrach signed a $4 billion oil and gas production deal with Italian, French and US majors in July, but experts have cast doubt over Algeria's ability to ramp up capacity in the short term.
In her interview with TSA, Borne noted that France does not depend heavily on natural gas, but said Paris wants to develop joint projects in the sector with Algeria "to increase the efficiency of its gas production capacity, which will increase its export capacity to Europe."
The European Union's energy commissioner Kadri Simson is also expected in Algiers on Monday and Tuesday.