Australia in 2021 cancelled a multi-billion dollar contract with a French firm to build the submarines.
It instead signed a new defence pact with the US and the UK, infuriating French President Emmanuel Macron.
He accused then leader Scott Morrison of lying to him, briefly recalling France's ambassador in protest.
Mr Albanese - who was elected in May - will travel to Madrid next week for the Nato summit. He will make a detour to Paris to smooth over ties.
"It is important that a reset occur," he told the Australian Broadcasting Corporation.
The relationship is key because France is not only a central power in Europe but - like Australia - in the Pacific too, he said.
"We've already had very constructive discussions… Next week's visit is a very concrete sign of the repair that's been done already," he said.
Australia earlier this month announced a €555m ($584m; £476m) settlement with France's Naval Group as compensation for scrapping the contract in favour of the Aukus deal.