I'm specifically interested in who the individual sailors were who crewed these missions. Were they private individuals? Employees of specific governments or companies? Who paid their wages?
/u/Ironhorn the Roi de France, François Ier ( 1494 to 1547) and l'Amiral Philippe Chabot (1492 to 1543), have charged you to:
voyager, découvrir et conquérir à Neuve-France, ainsi que trouver, par le Nord, le passage au Cathay de ce royaume ès Terres Neufves pour découvrir certaines ysles et pays où l'on dit qu'il se doibt trouver grant quantité d'or et autres riches choses.
Thankfully your friend (me!) translates that you are to travel, to discover and to conquer in New-France. Find by the North, the passage to the kingdom of China by Newfoundland and to discover certain islands and countries where it is said that one must find a large amount of gold and other rich things
You are one of the best sailors in France, you come from Saint Malo and since this is the 16th century you were born in 1491 and were reputed to be an excellent navigator by the time you were 20. Saint Malo is a great training ground for you, having very strong currents and extreme tides it produced some of the greatest sailors of the era, a tradition that continues to this day, if you ever make it over to France try and check out the route du rhum.
You travel a bit and pick up enough Portuguese to visit Africa and Brazil in 1526. When our King visits Mont Saint Michel in 1532 you meet him and are presented as the best candidate to explore the territory beyond Newfoundland, where Breton fishermen have been fishing for 20 or 30 years.
You face opposition from the ship owners of Saint Malo who believe your mission will be less fruitful than the Cod Fisheries which they exploit and from which this expedition will take men and materials.
Thankfully the King has your back, possibly because of the returns of other European nations from exploitation of the new world, and an embargo is put on the fishing boats to get men for the first 2 expeditions. You visit the Saint Lawrence and bring back some natives which, while no big deal to you, future generations will consider to be a massive human rights violation.
Your third expedition is known for returning with rocks that you believe to be, but are not, diamonds. This will lead to the expression faux comme diamants de Canada or fake as Canadian diamonds and you retire to your farm a short distance from Saint Malo. Your farm, while being sweet, is nowhere near as classy as the malouinières that will be built by rich merchants from Saint Malo in the XVII and XVIII centuries. You die without your portrait being taken.
You were the head of the first European expedition to visit the Saint Lawrence, in 2018 French people will be saying you discovered Canada. Since there were natives there this is incorrect. You will have a statue built of you in Saint Malo and when the city is rebuilt, following its destruction in 1944 during the liberation of Brittany by Pattons 3rd army, your tomb will be found and moved to a central position in the Saint Malo cathedral. A bridge will be built in your name in Montreal that /u/VivaTheBZH always gets stuck in traffic on. You become retroactively famous, compared to your contemporaries, because of the importance of Quebec in French history.
You are Jacques Cartier! We know way more about you than the crew of fishermen who were ordered to accompany you on this voyage.
Sources: Societe d'histoire et d'archéologie de saint malo: Annales 2014 pp 138
Saint Malo Gilles Foucqueron 2011 pp 38-48