Nous avons beau marcher doucement, son genou reste gonflé depuis le match d’hier.

It is a fixed expression meaning something like to do something in vain, however much one does something, or even though one tries.

So:

Nous avons beau marcher doucement...
means roughly:

• No matter how gently we walk...
• Even though we walk carefully...
• We may walk gently, but...

The idea is that the effort does not change the result.

Because in avoir beau, beau is part of an idiom. In this expression, you should not translate it literally as beautiful.

So it is best to learn avoir beau as a whole chunk:

• j’ai beau essayer = I may try / I try in vain
• tu as beau expliquer = even though you explain
• nous avons beau marcher doucement = even though we walk gently

In short: here beau does not mean beautiful.

Because the expression is always built with the verb avoir, not être.

It changes according to the subject:

• j’ai beau
• tu as beau
• il/elle a beau
• nous avons beau
• vous avez beau
• ils/elles ont beau

So nous avons beau marcher is the correct form for we.

Because avoir beau is followed by an infinitive.

Structure:

subject + avoir (conjugated) + beau + infinitive

Examples:

• J’ai beau attendre...
• Elle a beau parler...
• Nous avons beau marcher...

So in your sentence, marcher is in the infinitive because it names the action being attempted.

Because marcher is a verb, so it needs an adverb, not an adjective.

• doux / douce = adjective
• doucement = adverb

So:

• un pas doux = a gentle step
• marcher doucement = to walk gently / carefully / slowly

Here doucement describes how they are walking.

Yes, often it can. But doucement is a little broader than plain slowly.

Depending on context, it can suggest:

• gently
• carefully
• softly
• slowly

In this sentence, doucement probably suggests walking in a way that does not aggravate the knee—so gently or carefully may fit better than a simple slowly.

Both are possible, but they are not exactly the same.

• est gonflé = is swollen
• reste gonflé = remains swollen / is still swollen

Rester + adjective emphasizes that the condition continues and has not improved.

So here, son genou reste gonflé suggests: despite walking carefully, the knee is still swollen.

This is a very common difference between French and English.

In French, if something started in the past and is still true now, you usually use the present tense with depuis.

So:

son genou reste gonflé depuis le match d’hier

literally uses the present, but in English we often say:

• his/her knee has been swollen since yesterday’s match
• his/her knee has remained swollen since yesterday’s match

So the French present tense here is completely normal.

Here depuis means since.

It marks the starting point of a state that continues up to the present.

So:

• depuis le match d’hier = since yesterday’s match

More generally:

• depuis + point in time/event = since

  • depuis hier = since yesterday
  • depuis le match = since the match

• depuis + duration = for

  • depuis deux jours = for two days

Because de becomes d’ before a vowel sound.

So:

• de + hier → d’hier

This is a normal spelling rule in French.

Other examples:

• d’accord
• d’habitude
• d'amour

So le match d’hier simply means yesterday’s match.

Because the possessive adjective agrees with the thing possessed, not with the gender of the owner.

Genou is a masculine singular noun, so you use:

• son genou

This can mean:

• his knee
• her knee

depending on context.

Compare:

• son genou = his/her knee
• sa jambe = his/her leg

because jambe is feminine.

It can mean either his or her.

French possessive adjectives do not tell you the gender of the owner here. They agree with the noun that follows:

• son genou = his knee / her knee
• sa cheville = his ankle / her ankle

Only the context tells you whether the person is male or female.

Because the subject nous and the possessive son do not have to refer to the same person.

The sentence means that we are walking gently, but his/her knee is still swollen. That is perfectly possible: maybe we includes the injured person and another person, or maybe the group is moving carefully because of one person’s injury.

So grammatically:

• nous = the people doing the walking
• son genou = one person’s knee

They do not have to match.

That is true in many cases, especially when the owner is already clear from the grammar.

For example:

• Il s’est blessé le genou. = He hurt his knee.

French often uses le/la/les with body parts when a reflexive structure or indirect object already shows whose body part it is.

But here, there is no such structure making the owner obvious, so the possessive is natural:

• son genou reste gonflé

That clearly identifies whose knee is being discussed.

Here gonflé is functioning as an adjective meaning swollen.

It agrees with genou, which is masculine singular, so we get:

• gonflé

If the noun changed, the adjective would change too:

• la cheville reste gonflée
• les genoux restent gonflés

So in this sentence:

• genou = masculine singular
• gonflé = masculine singular form

It is masculine:

• un match
• le match

So:

le match d’hier = yesterday’s match

That is why the sentence uses le.

A natural English version would often be something like:

• No matter how gently we walk, his/her knee is still swollen from yesterday’s match.
• Even though we walk carefully, his/her knee has remained swollen since yesterday’s match.

The biggest differences are:

1. avoir beau usually becomes something like even though, no matter how, or in spite of trying.
2. French uses the present tense with depuis, while English often uses has been or has remained.
3. reste gonflé is often best translated as is still swollen or has remained swollen.