Relations between France and the country it colonised for 132 years have "never been so relaxed", according to the French presidential palace ahead of Hollande's second trip to meet Bouteflika.
The 78-year-old Algerian president's health is poor, following a stroke that sent him to a French hospital for three months in 2013.
Despite that, he was reelected for a fourth term in April.
The Algerian economy is also under strain, thanks to the fall in the price of oil, which nets 95 per cent of its foreign earnings.
But France, since 2013 the country's second trading partner after China, did 10.5-billion-euros-worth of trade with Algeria in 2014 and 450 French companies operate there.
Paris also wants to keep Algiers onside in the Malian conflict.
Thanks partly to Algerian mediation, the Tuaregs signed a provisional peace agreement in Algiers in May but are still bargaining about a definitive deal.
Algeria has another troubled neighbour to its east.
Algiers fears the conflict in Libya will spill over onto its territory and it has also led to a flood of arms and fighters over the border to Mali and neighbouring Sahel countries, while Europe has seen an increase in migrants crossing the Mediterranean from the wartorn country's shores.