What’s happening here in English is that you have an infinitive clause serving as a noun phrase. Since it is acting a noun phrase, it can be used anywhere a noun can be used, including as the object of a verb, as the subject of a sentence, as the object of preposition, or (nearly) anywhere else a noun is called for.
This happens all the time.
- I want to say something in French.
- To speak French is to love it.
- It’s easy to speak French.
In those examples, the infinitive clause has no expressed subject. What’s happening in your case, however, is that the infinitive clause has its own distinct subject.
- I want Pierre to speak French.
- It’s easy for Pierre to speak French.
In English, the subject of non-finite verb clauses takes the object case when a pronoun is involved.
- I want him to say something in French.
- Pierre wants me to say something in French.
- It’s easy for him to speak French.
What you have stumbled upon here is that in most Romance languages, including not just French but also Spanish, Italian, and dozens of others, infinitive clauses cannot take an expressed subject. Instead, you need to make a tensed subordinate clause starting with that. When you do this in Romance, the subject is again in the subject case when it’s a pronoun, unlike the object case used for non-finite subjects in English.
Compare these:
- I want him to say something in French.
- Je veux qu’il dise quelque chose en français. (French translation)
- Quiero que él diga alguna cosa en francés. (Spanish translation)
- Quero que ele diga alguma coisa em francês. (Portuguese translation)
Since you are studying French, you will need to get used to making tensed subordinate clauses whenever you would in English have an infinitive clause with a subject. Just to make it even more fun for you, these tensed subordinate clauses are often in the subjunctive mood, as shown above.
If, however, you were instead studying Portuguese, Galician, or Sardinian, then you would be allowed to used an infinitive clause with an expressed subject, provided it were not following a that, like when it’s the object of a preposition. Known as the personal infinitive, this peculiar construction has an infinitive that’s actually inflected for number and person (but of course not for tense or mood), and it takes subject pronouns not object pronouns the way it does in English. This makes it more convenient for English speakers first learning those languages.
But since you’re studying French not Portuguese, you don’t get to use that nifty construction, and so it’s necessary that you should become accustomed to saying things like this — rather than for you to be become accustomed to saying things like this.