The move signals a shift by Norway, long a staunch Atlanticist that has relied heavily on NATO and the US nuclear umbrella, towards closer defense cooperation within Europe.
Macron and Stoere announced the plan at a meeting in Paris, where they also signed a broader defense agreement which includes Norway joining a French-led nuclear weapons initiative, Reuters reported.
Stoere said Norway's primary deterrence would remain the NATO alliance and the United States, but described France's nuclear capabilities as "an important contribution" to the alliance's overall posture.
"France's capabilities are an important contribution to NATO's deterrence posture, which is important for us," Stoere said.
Under the plan, Norway would take part in what France calls "forward nuclear deterrence", under which European partners are more closely involved in French strategic thinking on nuclear defense.
"This agreement establishes a principle of mutual assistance between our two countries," Macron said, adding that deeper cooperation would support Europe's ambitions for greater strategic autonomy.
The initiative comes as European countries seek to strengthen their own defense capabilities amid doubts about long-term US commitments and heightened tensions with Russia.
In March, France offered to extend the protection of its nuclear umbrella to other European countries which, in practice, means that an attack on a country could trigger a French nuclear response.
Norway becomes the latest country to receive France's nuclear protection, after Poland and Lithuania.
Stoere told Norwegian news agency NTB earlier on Wednesday that no nuclear weapons will be deployed in Norway in peacetime.
The Nordic nation of 5.6 million inhabitants is a member of NATO, but not of the European Union.
"This closer cooperation will make European and transatlantic security stronger. Together, we are enabling a burden shift. It was long before Trump that this became necessary, that Europe had to pay more and do ... wiser investments, not only country by country, but coordinated," Stoere said.
Russia and the US are the world's biggest nuclear powers, with over 5,000 nuclear warheads each. China has about 600, France has 290 and Britain 225, according to the Federation of American Scientists.