I had written a timeline about what would have happened had France's initial attempts at colonisation in North America during the 16th century succeeded. If France's colonisation had begun at that time and even if they only sent a net of 15,000 settlers during the next century and a half, their numbers would have been nearly 300,000 by 1700 and 2 million by 1775, hardly a Herculean task. By comparison, the British colonies had 220,000 European settlers in 1700, and 1.7 million (excluding Quebec) by 1770.
Most permanent settlers could have been indentured servants, in addition to small numbers of soldiers given land grants. The colony could be a dumping ground for criminals accused of hunting illegally on nobles' or royal lands, along with men ignoring the salt tax or selling black market salt. For women they only need orphans and women from the poor houses of the cities, and not in great numbers.
Considering how well the French held up against the British during until 1758 during French-Indian War despite being outnumbered 16 to 1, imagine if their numbers equalled or slightly outnumbered the British. The French habitants were required to undergo military training, one which was far more extensive than that in the British colonies. I'd imagine with the outbreak of the first Anglo-French War, the French would simply overrun the British settlements, at least in New England. IOTL the English occupied Quebec in 1629, a settlement with a fewer than 200 Frenchmen, New England had some 1,800 English settlers at the time. If the French had successfully sustained a colony since 1541, their population would number around 50,000 to 70,000 by 1630. In that scenario, if English settlement in New England does occur, it would be simply overrun.