Il vaut mieux mettre de la crème solaire avant de nager, même quand le ciel est gris.

Il vaut mieux is a very common French expression meaning it is better to..., it's best to..., or sometimes you'd better....

So:

• Il vaut mieux mettre de la crème solaire... = It’s better to put on sunscreen...

It gives general advice in a natural, idiomatic way.

Here il is an impersonal subject. It does not mean he.

French often uses an impersonal il in expressions like:

• Il faut = it is necessary / you must
• Il pleut = it is raining
• Il vaut mieux = it is better

So in this sentence, il is just part of the structure. It does not refer to anyone.

Vaut is the third-person singular present form of the verb valoir.

• valoir = to be worth / to be better in certain expressions
• il vaut mieux = it is better

Because the subject is the impersonal il, French uses the third-person singular form:

• il vaut

This is an idiomatic expression, so it is best learned as a whole: il vaut mieux.

Because the normal pattern is:

• il vaut mieux + infinitive
• il vaut mieux faire quelque chose
• il vaut mieux attendre
• il vaut mieux mettre de la crème solaire

So mettre comes directly after il vaut mieux.

A different structure is also possible:

• Il vaut mieux que + subjunctive
• Il vaut mieux que tu partes maintenant. = It’s better that you leave now.

But with a general action, French usually uses il vaut mieux + infinitive.

Yes, mettre literally means to put, but in this context it means to put on or to apply.

So:

• mettre de la crème solaire = to put on sunscreen = to apply sunscreen

French often uses mettre for things you wear or apply:

• mettre un chapeau = to put on a hat
• mettre du parfum = to put on perfume
• mettre de la crème solaire = to put on/apply sunscreen

Because crème solaire is treated here as a substance, not as one specific identifiable item.

French uses the partitive article for an unspecified amount of something:

• du
• de la
• de l'
• des

So:

• mettre de la crème solaire = put on some sunscreen

That is why de la is used.

Compare:

• La crème solaire est importante. = Sunscreen is important.
  Here la crème solaire means sunscreen in a general sense.

• Mets de la crème solaire. = Put on some sunscreen.
  Here it is a quantity of a substance being applied.

Because after avant when the next verb stays in the infinitive, French uses de:

• avant de partir = before leaving
• avant de manger = before eating
• avant de nager = before swimming / before going swimming

So the pattern is:

• avant de + infinitive

This is very common in French.

French often uses an infinitive where English uses an -ing form.

So:

• avant de nager literally = before to swim but naturally = before swimming

This is a common difference between the two languages.

More examples:

• après avoir mangé = after eating
• sans parler = without speaking
• avant de dormir = before sleeping

So for an English speaker, it helps to remember that French often prefers the infinitive in these structures.

No, they are different.

• même quand = even when
• quand même = all the same / anyway / even so

In your sentence:

• même quand le ciel est gris = even when the sky is gray

That is not the same as quand même.

Compare:

• Même quand il pleut, je sors. = Even when it rains, I go out.

• Il pleut, mais je sors quand même. = It’s raining, but I’m going out anyway.

This is a very important distinction.

Yes, you could, but the nuance is a little different.

• même quand = even when
  This often suggests a real or repeated situation: whenever this happens.

• même si = even if
  This often sounds more conditional or concessive.

So:

• même quand le ciel est gris = even when the sky is gray
  This fits well with general advice about something that does happen regularly.

• même si le ciel est gris = even if the sky is gray
  Also correct, but slightly more focused on the condition itself.

In a sentence like this, même quand sounds very natural.

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

• le ciel est gris = the sky is gray
  This describes the appearance of the sky directly.

• il fait gris = the weather is gray/gloomy
  This describes the general weather.

In this sentence, le ciel est gris is a clear, concrete way to say that the sky looks gray or cloudy, which is relevant because people may wrongly think sunscreen is unnecessary in that situation.

It gives general advice.

French often uses impersonal structures like il vaut mieux to talk about what is generally advisable, without naming a specific person.

So the sense is:

• In general, it’s better to put on sunscreen before swimming, even when the sky is gray.

If French wanted to address one person more directly, it might say something like:

• Tu ferais mieux de mettre de la crème solaire... = You’d better put on sunscreen...

But your sentence is more neutral and general.

Yes, crème solaire is the normal everyday term for sunscreen or sun cream.

Even if the product is technically a spray or lotion, people often still say crème solaire in general conversation.

Examples:

• Tu as de la crème solaire ? = Do you have sunscreen?

• N’oublie pas la crème solaire. = Don’t forget the sunscreen.

So this is a very useful phrase to remember.