This may be the official policy, however it can be possible, at least I have an experience with KL/MH and I would guess it works the same for AF.
Checking in for ZRH-AMS-SIN 1 year ago. I had a separate ticket on MH to KUL with a long enough layover to re-check my bag. During check-in in ZRH it was proactively offered to check the luggage through to KUL. This came up because my spouse needed a TWOV for SIN, so the agent needed to add the information about the connecting flight to the system and then proactively offered to check the luggage through to KUL - although luggage was on my name and I was prepared to do SIN-immigration and re-check the bag.
Of course for a connection on separate tickets, I would expect for the worst to re-check luggage, however I would not exclude the possibility to have bags checked through to SQ and would certainly ask during check-in. I'm sure it is possible, however question is whether the policy (and training of the check-in agents) allows it.
It is of course technically possible to check bags through on separate tickets, it takes literally 30 sec to do it. With some softwares like Altea DCS system, it is even proposed automatically to the agent. But most airlines has an official policy to not do it, except sometimes within their alliance partners (but not always or not with all of them). Your example in ZRH is clearly a nice exception. Of course there is no risk to ask, but it's very unlikely they will say yes. My own experience with AF in CDG in 2025 : AF to PG (BKK) and AF to SA (JNB) : 2 big no, even for an Ultimate member. It is sometimes easier from outstations, especially in Asia, but it's getting harder too. I recently faced a refusal in VFA flying Airlink to JNB and connecting to AF on a separate ticket.
I said above that Altea is proposing automatically to do it, but I even suspect AF to have disabled this functionalitiy to avoid some agents accepting to do it for some pax. I say that because, for the AF to PG example I gave, the check-in agent really tried to do it. She managed to add the 2nd PNR but the system blocked her to validate the 2nd flight and bag label.
However, intra AF/KL or AFKL to DL or DL to AFKL always works.
I have upcoming itineraries CDG-SIN-CGK (1 ticket, but last leg on SQ with SQ flight number - no AF codeshare) and will expect that my luggage will be checked through given that it is on 1 ticket.
In that situation, you bag will be checked through without any problem.