How do I tell whether to use 'le' or 'la'?

Nouns in French are divided into two categories. With nouns in the first category, the word for the is le and for nouns in the second category it is la. The two categories are generally called masculine and feminine. The names masculine and feminine are conventional and probably stem from the fact that some masculine nouns refer to male people or beings, and some feminine nouns to female people or beings. But in the vast majority of cases, there is no real relationship between a noun's meaning and its gender. Consider, for example, that bureau and office can have similar meanings, but the former is masculine and the latter feminine; or that the noun personne is feminine but can refer to both men and women.

When you very first start learning French, you'll probably learn whether a noun is masculine or feminine by learning it with the word le or la: le garçon, la fille etc. Initially, this is probably the most effective way of learning when to use le and when to use la.

In other words, the answer to our question to start with is "you've just got to remember!".
Rules and patterns for deciding on the gender of a French noun

As your proficiency in the language grows, you'll probably reach a point where you stop learning words with the article le or la alongside. For example, if you're acquiring vocabulary through reading or watching a film, some of the time the article won't be present. And there'll inevitably be times when you can't quite remember the gender of a word and could do with some kind of "best guess". The following table gives some general patterns that will help you decide whether a word is masculine or feminine.
Generally masculine Generally feminine
Nouns referring to male people. Nouns referring to female people.
A handful of nouns are masculine, whatever the gender of the person they refer to, e.g.: amateur, auteur, témoin, vainqueur, voyou plus certain job titles. These are feminine, whatever the gender of the person: personne, victime, recrue (recruit), connaissance (acquaintance).
Certain nouns referring to animals that can refer to only the male of the species. For example: étalon (stallion), cerf (stag), matou (tomcat). Certain nouns referring to animals that can refer to only the female of the species. For example: chatte (female cat), chienne (bitch), louve (she-wolf).
Masculine nouns that are 'generic' terms and can refer to either a male or female of the species. For example, le cheval can refer to either a male or female horse. Feminine nouns that are 'generic' terms and can refer to either male or female of the species. For example, la souris can refer to either a male or female mouse.
Names of towns. Other place names (departments, rivers, countries) not ending in -e. Place names ending in -e.
Common exceptions: le Mexique, le Combodge, le Rhône, le Finistère (French department), le Zimbabwe (-e pronounced). Common exception: la Franche-Comté (French department). Sometimes town names, especially if they look or sound feminine (e.g. Marseilles ending in -es), can be treated as feminine. This is quite rare, though.
Nouns ending in:

* -age
* -ment
* -il, -ail, -eil, -ueil
* -é (but not -té)
* -eau and -ou
* -ème, -ège
* -i, -at, -et and -ot
* -er
* -oir
* -isme
* -ing
* -ard
* Words ending in other consonants (in the spelling).

Nouns ending in:

* -tion, -sion and -son
* -ure
* -ude, -ade
* -ée
* -té
* -ière
* Consonant followed by -ie
* -euse
* -ance, -ence
* Most other endings consisting of Vowel + Consonant + e: -ine, -ise, -alle, -elle, -esse, -ette etc

Nouns ending in -eur, generally derived from a verb, denoting people or machines carrying out an activity: aspirateur, facteur, ordinateur Figurative nouns ending in -eur, usually derived from an adjective: rougeur, largeur, pâleur, couleur, horreur, rumeur
Principal exceptions (look feminine but actually masculine): cimetière, episode, espace, intervalle, lycée, magazine, mille, musée, réverbère, silence, squelette, stade Principal exceptions (look masculine but actually feminine): cage, eau, image, merci, page, peau, plage
Compound nouns of the form verb-noun: porte-monnaie, pare-brise, tire-bouchon. --
Common rules and patterns for deciding if a French noun is masculine or feminine.

Where there is a conflict, rules to do with a word's construction or function generally override rules to do with the word's sound or ending. For example, pare-brise ends in the normally feminine ending -ise, but is of the form verb-noun so is masculine. The words trompette and clarinette have a feminine ending, but when used to denote a person ('trumpet player' or 'clarinette player'), they are masculine.
Further reading...

Correct Your French Blunders

The chapter on Nouns (pp. 35 onwards) gives a simplified list of the most common endings and their typical genders, along with some common examples.

Comprehensive French Grammar

See sections 47 onwards (pages 34 onwards) for a comprehensive list of rules determining gender plus a comprehensive list of examples and exceptions for each rule. Note that in some cases, a number of Price's are covered by a single rule in the table above.

Le ou La?: The Gender of French Nouns (M. Surridge, 1995)

See this book for a thorough treatment of the subject of noun gender in French, with practical advice from a teaching and learning point of view.

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