That would see the current population of 67.4 million rise to a peak of 69.3 million before reversing, the INSEE agency said in delivering forecasts for the next 50 years.
The forecast assumes a continued fertility rate of around 1.8 births per woman, already one of the highest in the European Union.
It also foresees new arrivals compensating for a projected decline in births starting in 2035.
France and other Western nations have seen a steady erosion of fertility rates over the past decade as fewer women have children and families have got smaller.
For years the government has tried to encourage births by offering family allowances and heavily subsidised child care, while also providing bigger tax breaks for larger families.
But its fertility rate remains below 2.1, the threshold experts say is needed to maintain population levels.
INSEE said that if the rate increased to 2.0, France would have 4.1 million more people by 2070 compared with its central forecast.
An “inevitable” development by 2040, however, will be “a continued ageing of the population,” the agency said.
By then, there will be an estimated 48 to 53 retirees over 65 for every 100 working-age adults, up from 37 currently.