In the trade this part is generally called "belly fairing" because that term is shorter and more specific than older names like "center wing fairing" or "wing-to-body fairing" or "wing/fuselage fairing". See this AV article about an AD for the A380, for example.
Belly fairing expresses better that the fairing is mostly below the wing-fuselage intersection. The older expressions were already used for the usual fillets between wing and fuselage which became standard in the 1930s. When it was learned that in transsonic flow the clever shaping of displacement bodies can reduce drag, the fairing grew over time. An important benefit is the added space for storing the main gear.
The usual French name for it is "carénage ventral", which is a pretty straightforward translation of the English expression.