It would be difficult to believe these two expeditions were not coordinated in some manner, particularly since many of the principles had been schooled in Saumer, a town that became the site of the greatest of the Huguenot fortresses in the Religious Wars.
Many of my French ancestors ended up settling sites named in DeSoto's elaborate journals including the only place in the Ohio Valley that had any appreciable quantity of gold. They did this under the authority of the King of France and with the permission of their cousin, the King of Spain although at that time the King of Spain had ceded his claims to the Eastern Seaboard to his cousin, the King of England.
The Sea to Sea grants were given in good faith by the King of England (Scotland, etc.) because no one had yet taken a good look at the West Coast although the English already had as good a claim to California as anyone, and possibly more since Sir Francis Drake discovered San Francisco Bay in 1579.
As you no doubt recall, the King of Spain, hand in hand with his sister the Church, did not build a mission in California until 90 years later. Amazingly they all claimed serious problems with the weather. Cabrillo, who reported some West Coast adventures in 1542, left those reports behind. He also appears to have MISSED San Francisco Bay.
As you can see the early discoveries concerning the West Coast (the other end of the Sea to Sea claims) are shrouded in mystery and intrigue. But the only conclusion that can be drawn is that His Catholic Majesty, the King of Spain, didn't have as clear a title to the West Coast as some today presume, and absolutely nobody can believe Cabrillo's claim that Southern California was racked with storms.