What is the name of the starship in Star Trek: Insurrection that transports Picard's crew?

The starship transporting Picard's crew in Star Trek: Insurrection is the USS Enterprise-E.

The Enterprise-E is the Sovereign-class flagship introduced in Star Trek: First Contact. In Insurrection, Captain Jean-Luc Picard and his crew become involved in a conflict over the Ba'ku homeworld. The planet's metaphasic radiation gives its rings unusual restorative properties, making the region valuable to outside powers.

Picard discovers that Starfleet officers are cooperating with the Son'a to remove the Ba'ku from their home. He refuses to accept the forced relocation and places the Enterprise in opposition to the operation. The ship serves as both a diplomatic platform and a combat vessel during the crisis.

The Enterprise-E should not be confused with the Enterprise-D, which was destroyed in Star Trek: Generations. Both ships are commanded by Picard, but they belong to different classes and have different histories.