The country is Lebanon with 38% of its population being Francophone. And that one country is the small country of Vanatu, where 32% of the country's population of 270.000 speak French. As you might have been able to gather from the above, the French language is present all around the world.
More than 75 million people speak French as their first language and an impressive 200 million speak the "language of romance" as a second language. The French language shines in the field of language learning. It is the second (or third) most studied language in the world and has about 120 million active learners at the moment!
18 of the 29 most francophone countries and 50% of the world's French speakers are in Africa. These countries are Mauritus, Gabon, Congo-Brazzaville, Seychelles, Tunisia, DR Congo, Djibouti, Cameroon, Togo, Morocco, Benin, Côte d'Ivoire, Algeria, Equatorial Guinea, Central African Republic, Comoros, Senegal and Guinea.
These are France (obviously), Monaco, Luxembourg, Belgium, Andorra, Switzerland and Portugal. With the exception of Portugal, which has about 25% French speakers, all of the other countries have over 65% of people who speak French, which means that you'll have no trouble getting by only with the French language.