In OTL Hugenots were forbidden to travel to Nouvelle-France in 1628, let’s do the opposite.
In 1680, Louis XIV decides, on the advice of Jean Talon, the former Intendant of New France, and Vauban to deport as many french Hugenots as possible to Nouvelle-France to work as forced indentured laborers and workers for a duration of 12 years (twice the normal period of engagisme). After this period they are free to settle, wherever they want, and to obey to the King. It’s either death or exile to Nouvelle France.
Colbert reluctantly accepts this plan, preferring to see Huguenots in French colonies, rather than providing wealth to other countries like England, the United provinces of Netherlands or to the German states. Many Huguenots occupied important places in society from merchants, craftsmen, to soldiers and nobles.
Colbert was also afraid of secession, as Huguenot presence was heavily concentrated in the western and southern portions of the French kingdom, as nobles there secured practise of the new faith. The Camisard revolt in 1685 reinforced this fear and reminded him of the past civil wars based on religion. An English intervention to help those revolters would be a disaster.
Rumored Hugenots are marked with a branding iron by royal officers and priests, so they can’t flee out of the Kingdom before their deportation. This Fleur de Lis marking will turn into an universal symbol of Hugenot faith with some fringe Hugenot groups continuing to iron brand themselves nowadays, centuries after the deportation.
It’s better and more economically useful than killing them on spot or pushing them to flee aboard. In Nouvelle-France, everything will be done to be sure that they become Catholics.
To be sure than their brethen reject their faith, King Louis XIV put their sons and girls into religious and military institutions to be trained as professional soldiers (catholic janissaries !) and good catholic spouses.
Parts of Hugenot population wouldn’t appreciate this situation and many of them would try to flee. In North America, those will be known as wood runners or "coureurs des bois" and mix with natives, slowly developing an unique culture.
I am sorry the links are in french
1.
https://fr.m.wikipedia.org/wiki/Engagisme
2.
https://fr.m.wikipedia.org/wiki/Engagisme_aux_Amériques
This policy of sending Hugenots to various colonies, especially to Nouvelle-France, won’t stop until the Edict of Tolerance signed by Louis XVI on 7 November 1787 and registered in the Parlement of Paris on 29 January 1788.
Gradually, groups of Hugenots and Coureurs des bois from Nouvelle-France will depart to create their own religious Republics in the west of Nouvelle-France. It’s the Great Travel or Grand Voyage.