Masamune is one of the best weapons of the game because of its high multi-hit rate and Genji Glove's effect. However, the Tournesol is just plain stronger and will deal more damage than the Masamune in a single hit. It also has a decent multi-hit rate as well. Without Genji Glove, the Masamune will score multiple hits less often, and the Tournesol will be able to beat it in terms of damage.
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I'm currently on a playthrough trying to complete most of the non-story stuff in the game, but your analysis has convinced me that it's just not worth getting the tournesol. I got the zodiac spear, and will get the masamune and excalibur, other than that i'll keep balthier on guns and my mages with staves/rods/maces/whatever.
Tournesol may be somewhat weaker than the Zodiac Spear, but it has higher evasion and a higher multi-hit rate. In most situations, Excalibur is better than Tournesol because of its Holy Element, but Tournesol will still be better if the enemy is not weak to, or absorbs Holy. Particularly, Yiazmat.
The only reason why you shouldn't get Tournesol is if you don't want to bother with getting all the required loot. It's definitely worth it though.