- For example, can a present infinitive serve as subject of a sentence? ("To be or not to be, that is the question.")
- How is (a) or (b) again different from de + infinitive as found, for example, in this sentence from Camus's The Stranger
"To be or not to be" is a clause in the infinitive, not a noun. Any infinitive clause can indeed be used as a subject in French. It can appear in two ways:
In the canonical subject position, without a preposition:
[Travailler avec eux] me fait grand plaisir (formal)
[Travailler avec eux] ça me fait vraiment plaisir (colloquial)
After the verb, doubled by a dummy pronoun (cela or il formally, ça colloquially) and introduced by the preposition de:
Cela me fait grand plaisir [de travailler avec eux] (formal)
Ça me fait vraiment plaisir [de travailler avec eux] (colloquial)
(Fun fact: plaisir itself started as a infinitive used as a noun, but this is not obvious to native speakers anymore since plaisir has been replaced by plaire as the infinitive and only lives on as a substantive)
- Do we distinguish (a) present infinitives serving as a noun and (b) nouns that only look the same as a present infinitive but are independent words in their own right?
Substantived infinitives used to, but cannot anymore, take personal or adverbial pronouns. They can't really be followed by a predicate either, but this is less clear cut.
(1) Ton rire m'a mis de bonne humeur (Your laugh made me happy) - Noun
(2) Rire m'a mis de bonne humeur (to laugh made me happy) - Verb
You can attach a pronoun to rire in (2), but not in (1).
(3) *Ton en rire m'a mis de bonne humeur - Gibberish !
(3) En rire m'a mis de bonne humeur - perfectly acceptable sentence
In short, a substantived infinitive acts in all ways as a noun, while an infinitive clause acts as a verb.
I'd also like to add a few titbits as a complement to the already very complete previous answers:
First is that the infinitif substantivé has been enjoying quite the comeback in the field of philosophy and psychology since the mid-19th Century, and is productively used by scholars in those disciplines.
Here a few citations (taken from BURIDANT Claude, la substantivation de l'infinitif en français in "Actes du XXVe Congrès International de Linguistique et de Philologie Romanes", 2009)
Je dis "poétique du traduire" plutôt que "poétique de la traduction pour marquer qu'il s'agit de l'activité, à travers ses produits"
Le s'entendre parler et le vouloir parler
La maîtrise, c'est précisément le "savoir-conduire" du faire.
(Notice how it contradicts what I said above about the pronouns, but this is limited to this particular usage, which sounds honestly a bit pedantic and ridiculous from outside the fields where it is used)
Another register where it is still somewhat productive is sports jargon: le toucher de balle.
Finally it is still quite common to create neologisms on the basis of le savoir-faire and le vivre ensemble: le savoir-mourir, le savoir-dire, le communiquer ensemble.
Second is that a relatively recent and immensely productive way of creating deverbal nouns of the first group verbs (those with the -er suffix) is to make their bare indicative present stem a noun:
L'entame du match (the beginning of the match, from entamer, to take the first bite of something, to begin something)
Jouer pour la gagne (play for the win, from gagner, to win)
C'est juste de la retape (It's merely cobbled together, from retaper, to refurbish)
Elle y a été à l'aguiche (She used her charms, or more literally, "She went at it in an enticing manner", from aguicher, to entice, to seduce)
An important difference between the new and old deverbal nouns is that nouns formed on the infinitive are always masculine, while nouns formed on the indicative are always feminine.