Croisée d'ogives (rib vault)

There is no connection whatsoever with croisée du transept (crossing).

A rib vault is in principle the same as a voûte d'arêtes (groin vault).
However, a rib vault can be a crossing of two barrel vaults as well as two pointed barrel vaults.
The difference with a groin vault is, that on the arêtes (cutting lines) of the two vaults load bearing ribs are applied, carrying the vault hoods.
With these sort of vaults the ogives (ribs) are built first, and only afterwards the hoods are installed spanning between these ribs.
In an ordinary groin vault these hoods are self supporting.

See also voûte d'ogives (synonym) and ogive. The picture shows the rib vaults in the cellier (warehouse) of the abbaye (abbey) of Cluny.

Cellier - Cluny