Here's a possible way to tie the stories together. It seems much more likely that the French explorers would have discovered and exploited gold placer deposits during their Colorado expedition rather than working a lode deposit. This type of scenario is what triggered the California gold rush and others - virgin placer streams were relatively easy to locate and work, with a lot of gold being recovered quickly. The underground lode deposits were found and worked later, and required more time and technology to be successful.
Let's say the French began finding gold in the streams near the Arkansas River headwaters, then moved to westerly, possibly as far as the Elk Mountains mineral deposits
(Treasure Mountain 1). The map below shows a highly generalized theoretical route, passing through several areas that proved later to be big producers in Colorado. If the French were the first to discover some of these areas, the pickings could possibly have been easy and lucrative. By the time they circled their way south to the San Luis Valley area, they may have been toting a lot of gold and decided to cache it. Maybe that's where
Treasure Mountain 2 comes into play. From the mining district map, it's apparent that no significant mineral deposits have been worked in the Pagosa-Wolf Creek area. This doesn't support the rumor of a rich French mine there, but there would certainly be plenty of caching opportunities. This might explain the variation in the stories' locations - the French may have been active in all of them. Just an unproved theory.
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Colorado School of Mines map