Sodium sulfide does not react with sodium carbonate, but they react individually under acidic conditions.
What is the product of reaction between sodium sulfide and sodium carbonate? Sodium sulfide becomes sodium carbonate and sodium carbonate becomes sodium sulfide. Does this mean that there is no reaction? There is no metathesis reaction of the salts of the same metal cation.
Sodium sulfide and sodium carbonate are weak acid salts, and they will undergo metathesis under acidic conditions.