The Haitian Revolution ended with Haiti's independence from France.

prepositional phrase

participial phrase

gerund phrase

infinitive phrase

Since there are no infinitives, gerunds, or participles in this sentence, I'm assuming that the underlined phrase is with Haiti's independence from France.

This means that the phrase you are looking for is prepositional, since it begins with a preposition with (or from, if the underlined phrase is from France).