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:

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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?

Caption 57, Actus Quartier - Fête de quartier Python-Duvernois - Part 1

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On passe une super après-midi.

You spend a great afternoon.

Caption 90, LCM - Rétine argentique, le paradis des photographes

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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.

Caption 36, Cap 24 Paris - Alessandro fait les Puces! - Part 1

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Le temps présent fait partie du mode indicatif.

The present tense is part of the indicative mood.

Caption 10, Le saviez-vous? - Le mode indicatif, c'est quoi?

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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

Caption 3, Gaëlle - Librairie "Livres in Room"

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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.

Caption 27, Patricia - Pas de crédit dans le monde des clones - Part 2

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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.

Caption 4, Manon et Clémentine - Vocabulaire du livre

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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, euh, voir que les yeux.

So a niqab is a full-length veil that only, uh, shows the eyes.

Caption 10, Cap Caen Normandie TV - Danse - Héla Fattoumi se dévoile

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Il a une seule voile.

It has a single sail.

Caption 11, Fred et Miami Catamarans - Les Bateaux

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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.

Caption 20, Paris Tour - Visite guidée de Paris

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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.