I’d recommend the cheap flight to Singapore.
Scoot Business Class is basically premium economy. You can bid to upgrade an economy seat to business (I did this a couple years ago for a flight leaving Australia on a Saturday in August, and the upgrade cost less than $100pp which on top of a cheap economy fare was, well, inexpensive and worth it compared to Scoot cattle class).
I’d then recommend a business class bunny hop from Singapore to Europe via Istanbul (or any other Turkish city for that matter). Singapore and Turkish Airlines are both in the Star Alliance, and fly daily direct to Istanbul.
I’m not familiar with the ‘new’ Ataturk airport in Istanbul, but allow plenty of time to make a connecting flight – ‘old’ Ataturk was huge and very busy, and you will join at least one slow moving queue at passport/security control.
The onward flight into France from Istanbul doesn’t need to be premium class - or booked using FF points - because it is quite short (3.5 hours or so) and several airlines fly that route.
Plus, if you have some time to spare and are flexible, a stopover in Turkey is a good life choice!
(Istanbul is no less safe than Paris… and Turkey is hospitable, fairly cheap, and fascinating)
That said, if business class is your main priority you might be able to travel the French leg in business class for no extra cost, if in a single booking. I once redeemed a business class FF seat on Turkish Airlines from Singapore to Malta, via Istanbul [no stopover], and got charged the Istanbul redemption rate for the whole journey, rather than the European rate.