Learn French: La grand-mère est très fière de sa fille. - The grandmother is very proud of her daughter.

Fière is the feminine form of the adjective fier (proud). For adjectives that end in -er in the masculine, the feminine form changes to -ère. This adds a grave accent and an e at the end, which also changes the pronunciation so you clearly hear the "R" sound.

Why is it grand-mère and not grande-mère? Isn't mère feminine?

Yes, mère is feminine! But grand-mère is a special exception. Back in Old French, the adjective grand didn't change its spelling for feminine words. That older spelling froze in time for a few compound words like grand-mère (grandmother).

Does sa in sa fille agree with the grandmother or the daughter?

It agrees with fille (the daughter). In French, possessive words like sa (which can mean his, her, or its) always agree with the noun that is owned, not the person who owns it. Since fille is feminine and singular, we use sa.

Why do we use de after fière?

In French, the set phrase for "proud of" is être fier de (or être fière de for a female subject). The preposition de translates directly to "of" here, linking the feeling of pride to the person she is proud of.