Does a Haitian need a visa to travel to Cuba from Port-Au-Prince, Haiti?

While you need a visa, it's Cuba so there are loopholes. Everything has loopholes, that's what socialism is built on, I still remember. Check Timatic for more:

Visa required, except for Passengers with a Tourist Card (Tarjeta del Turista) issued to visitors traveling as tourists.

• Tourist Cards (Tarjeta del Turista) must be obtained prior to arrival in Cuba. They are available at:
  • Cuban Embassies or Consulates;
  • Authorized Airlines;
  • Travel agencies.

As per Havana Times Is a Tourist Card the same as a Tourist Visa?:

Mexicana, Cubana and other carriers usually require that the Cuban Tourist Card be purchased from them, at the airline check-in counter, before departure to Cuba.

While I can't find the information for Haiti, I have found this to be true from reports on TripAdvisor for Mexico, the consulate in columbia:

You can also purchase the visa or tourism card in the following places:

• If you travel by the airlines AVIANCA, COPA or CUBANA DE AVIATION , at the EL DORADO airport of Bogota, at the time of checking.

So you probably want to buy a plane ticket from Cubana to Havana or Santiago de Cuba. That's what you'd do anyways since no other company flies Haiti-Cuba direct. As per this TripAdvisor thread there are no ferries either (2016 summer).