"He is very happy to be reunited with his family."
Translation:Il est très heureux de retrouver sa famille.
the reason is because of the following constructs:
être heureux de quelque chose - to be happy about something
être heureux de faire - to be happy to do
Je serais heureux de vous rencontres.- I would be happy to meet you.
J'ai été très heureux de vous rencontrer. - It was very nice to meet you
Je suis très heureux de vous connaître. - I am very happy to know you
Je suis heureux de vous l'entendre dire. - I'm pleased to hear you say it.
Also note the construct être heureux que - to be pleased that, to be glad that
Nous sommes très heureux que vous soyez rétabli. - We are very glad you are better.
You confuse two things here.
The fact that there is "d' " before "être réuni" is because it's the mandatory contraction of "de" before a verb with a vowel. It has nothing to do with the verb "devoir (doit)" in your second example, which has no reason to be contracted in any way.
- "Il est temps d'aller se coucher."
- "Il doit aller se coucher."
Because "de" is a preposition, its use depends on how your sentence is structured. A preposition is used as a link between two clauses in a sentence.
It's the same in English :
- "Je doit être parfait." = "I must be perfect."
- "C'est impossible d'être parfait." = "It's impossible to be perfect."
Here "de" in French is replaced by "to" in English. They are both prepositions.
Isn't a simpler explanation just that "de" is needed in some constructions and not others i.e. it is never needed before the infinitive in a construction like your first example "doit etre", "aime manger", "peux chercher" but it is needed in others like your second example. :-)
"rencontrer" means to either come across someone, or to meet someone for the first time.
There are other less used figurative or literal meanings, such as opponents facing each other in sports or things like that, but "rencontrer" can't be used to mean that you reunite with someone.
It depends on which verb you tried it.
"retrouver" doesn't use a preposition on the object it refers to. We can't say "Je retrouve avec un ami.", but we say "Je retrouve un ami.".
If you want to make it simple to you, just remember that verbs in English and in French don't necessarily have the same structure. It's the same the other way around, we say "to look for ..." in English but in French it's simply "chercher ..." (and not "chercher pour ..."). You'll have to learn and remember the verbs as you use them for the first time, once you used them or saw/heard how they work, it's quite easy to remember them.