One Word, Two Genders

You may know that all French nouns are either masculine or feminine, but did you know that some nouns can be both? A word like après-midi (afternoon), for example, can be either masculine or feminine depending on the speaker's preference:

Vous deux, là, qu'est-ce que vous allez faire de beau cet après-midi?
You two, here, what are you going to do that's exciting this afternoon?
Cap. 57, Actus Quartier: Fête de quartier Python-Duvernois - Part 1

On passe une super après-midi.
You spend a great afternoon.
Cap. 90, LCM: Rétine argentique, le paradis des photographes

Un après-midi (masculine) and une après-midi (feminine) both mean "an afternoon." But usually, when a word's gender changes, its meaning changes too. Take the word mode, for example. La mode (feminine) means "fashion," but le mode (masculine) means "mode" or "(grammatical) mood":

Le milieu de la mode est aussi touché hein, forcément.
The world of fashion is also affected, you know, necessarily.
Cap. 36, Cap 24: Paris - Alessandro fait les Puces! - Part 1

Le temps présent fait partie du mode indicatif.
The present tense is part of the indicative mood.
Cap. 10, Le saviez-vous?: Le mode indicatif, c'est quoi?

Like mode, a lot of dual-gender words end in -e. Another common one is poste. When masculine, it means "post" as in "position" or "job" (among other things), and when feminine, it means "post" as in "post office" or "mail":

J'ai trouvé mon premier poste de libraire
I found my first bookseller position
Cap. 3, Gaëlle: Librairie "Livres in Room"

Si je venais à gagner, vous m'enverrez mon chèque par la poste.
If I were to win, you'll send me my check in the mail.
Cap. 27, Patricia: Pas de crédit dans le monde des clones - Part 2

You'll most often find the word livre in its masculine form, meaning "book." When feminine, it means "pound," as in the unit of weight and currency:

L'extérieur d'un livre s'appelle la couverture.
The outside of a book is called the cover.
Cap. 4, Manon et Clémentine: Vocabulaire du livre

Une livre équivaut à environ quatre cent cinquante-quatre grammes. 
One pound is equal to around four hundred fifty-four grams. 

Voile has related meanings in both its masculine and feminine forms. Both refer to things made of fabric—a veil (un voile) and a sail (une voile): 

Un niqab, c'est donc un voile intégral qui ne laisse voir que les yeux.
So a niqab is a full-length veil that only shows the eyes.
Cap. 10, Cap Caen Normandie TV: Danse - Héla Fattoumi se dévoile

Il a une seule voile. 
It has a single sail.
Cap. 11, Fred et Miami Catamarans: Les Bateaux

This video takes you on a tour (un tour) of Paris, making a requisite stop at the Eiffel Tower (la Tour Eiffel):

La Tour Eiffel, qui est le symbole de la France.
The Eiffel Tower, which is the symbol of France. 
Cap. 20, Paris Tour: Visite guidée de Paris

Gender can be tricky in French, doubly so when you're dealing with words that can be both masculine and feminine. Remembering them is just a matter of practice. You can find a comprehensive list of dual-gender words on this page.