From the AF baggage calculator:

CDG-DXB in Business is:

Your trip : France (Paris) - United Arab Emirates (Dubai)
In class : Affaires
Allowance type Number of baggage items
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You can travel with 3 baggage items of maximum 23 kg each


CDG-SIN doesn't show but I assume it is the same.

The key is - for the new rules - bags can not weigh more than 23kg or more then 50lbs each. So you need multiple small bags.

Also - USA to Europe check baggage is now:

Economy = 1 baggage items of maximum 23 kg each
Prem Eco = 2 baggage items of maximum 23 kg each
Bus/First = 3 baggage items of maximum 23 kg each

Again - no bag can weigh more than 23kg. And USA-Europe in Economy is only one bag.