Curricle

A curricle is a light two-wheeled carriage drawn by two horses abreast.

For park driving, such as in the Bois de Boulogne or along the seafront at Honfleur, two liveried mounted grooms might follow.

[1] In Latin, the word curriculum means "running", "racecourse" or "chariot".

[6][3]: 95  The danger, plus the development of the safer phaeton and cabriolet, replaced curricles as the fashionable carriage of the time.

Unfortunately it was rather dangerous if the horses shied or stumbled, and this tended to reduce the demand for it.