Mh I'm not a tax expert and neither French, so you should totally speak with someone that works with those things. What I can tell you is that
Singapore is in Grey zone so technically IRAS (tax authority in SG) should communicate to you are a shareholder in a SG company. But, because you are obliged of having a local director you are just a shareholder, so your name will appear only when someone run a pay check via ACRA website. As you are not the director, technically you should be entitle to pay only personal tax in France, and not the corporate, but take it with a pinch of salt, because I'm not sure about it, and for sure you need the opinion of a tax expert for this.