A narrative, by definition, is a written or spoken account of events which connect in time, place, or meaning. Examples of narratives are fables, legends, fairy tales, short stories, and novels. Given that a speech is a public discourse (one's thoughts, or knowledge, on a subject), one could state that a speech can be a narrative given that a speech can be used to detail one's thoughts on a subject through including a narrative (spoken story) to prove a point.
Therefore, if looking at the formal definition of a speech, many speeches are meant to inform, persuade, or instruct. If the narrative used is meant to do any of these things, a narrative exists within the speech. If one is simply telling a story, then it would not necessarily be a speech; instead, it would simply be a narrative which is spoken.