Called Dragons in French because of the gun they used to carry made them look like Dragons, or so goes the story.
We heard a rumour long ago before the internet that there was a dragoon reenactment group in France for this period. It turned out not to be true alas. It would certainly be a colourful thing but I suppose as expensive as some of the more glamorous options. French dragoons of this period are perhaps associated with the dragonnades - forcible billeting of dragoons on Protestant families. The picture at the top by Guerard is worth closer inspection as it's thought to depict a forcible billeting. It was a terrible thing for these families but it's a long time ago now. I'm cynical enough to think that would actually make a good scenario for an event - going round a village and forcibly billeting yourself in some poor unfortunate's house. Maybe not. Presumably dragoons weren't the gentlemen of the French cavalry for them to be used in this role being more of the vulgar fellows of the infantry.