Why is it 'mon amie' if amie is feminine?

Before a feminine noun starting with a vowel or silent h, French swaps ma / ta / sa for mon / ton / son. The reason is purely phonetic - 'ma amie' would force two vowels together, so French uses the masculine form to bridge them. The noun stays feminine, so the adjective still agrees as feminine ('mon amie est francaise'). The same rule applies to ton (ton ecole) and son (son histoire).

How do I say 'his' versus 'her' in French?

You don't, separately. French son, sa, ses cover both his and her - the agreement is with the thing possessed, not the possessor. Son livre means both 'his book' and 'her book'; sa maison means both 'his house' and 'her house'. If the context is genuinely ambiguous, French reaches for the workaround 'le livre de Marie' or 'son livre a elle', but day-to-day, son and sa carry both meanings without any signal of the possessor's gender.

French Possessives

French possessive adjectives sit before the noun and agree with the thing possessed. The gender of the possessor is invisible in French - son and sa mean both his and her, depending on what's possessed.

The full table

Possessor	Masc sg / vowel-fem	Feminine sg	Plural
je (my)	mon	ma	mes
tu (your, informal)	ton	ta	tes
il / elle / on	son	sa	ses
nous (our)	notre	notre	nos
vous (your)	votre	votre	vos
ils / elles (their)	leur	leur	leurs

Fifteen forms. The split is clean:

mon / ton / son mark gender and number (three forms each).
notre / votre / leur only mark number (two forms each).

The mon-before-vowel rule

Before a feminine noun starting with a vowel or silent h, French uses mon / ton / son instead of ma / ta / sa. The noun is still feminine; the adjective is using the masculine form for pronunciation only.

mon amie (my female friend) - not "ma amie"
ton ecole (your school) - not "ta ecole"
son histoire (his / her story) - not "sa histoire"
mon habitude (my habit)

When an adjective intervenes and starts with a consonant, the feminine form comes back:

ma bonne amie (my good female friend) - amie is now buffered by bonne

This is one of the small French rules that's mandatory and that no one will teach you twice. Get it right and your French sounds native; get it wrong and it sounds like you've just started.

Agreement with the thing possessed

The possessive matches what's owned, not who owns it.

mon pere (my father - masculine singular)
ma mere (my mother - feminine singular)
mes parents (my parents - plural)
notre fille (our daughter - feminine singular)
leurs enfants (their children - plural)

A father and a mother both say mon fils (my son) and ma fille (my daughter), because the agreement is with the child's gender, not the parent's.

The son / sa ambiguity

Son livre could mean his book or her book. French doesn't distinguish, and most of the time context makes it obvious.

When it genuinely doesn't, French reaches for a lui / a elle as a clarifier:

son livre a lui (his book - specifically his)
son livre a elle (her book - specifically hers)
le livre de Marie (Marie's book - just naming her)

Day to day, plain son / sa / ses carries the load without anyone needing the disambiguation.

Worked examples

Ma mere habite a Paris. (My mother lives in Paris.)
Ou sont tes cles? (Where are your keys?)
Notre maison est petite. (Our house is small.)
Ses enfants etudient a Londres. (His / her children study in London.)
Mon amie Sophie est medecin. (My friend Sophie is a doctor.)
Leurs idees sont interessantes. (Their ideas are interesting.)

Body parts: French uses the definite article

A quirk worth flagging. French often drops the possessive for body parts, swapping it for a definite article plus a reflexive pronoun.

Je me lave les mains. (I wash my hands. Literally: I wash myself the hands.)
Il s'est casse le bras. (He broke his arm.)
Elle a mal a la tete. (She has a headache.)

Saying je lave mes mains is grammatical but sounds wrong. The article + reflexive is the native default.