From a modern point of view it is preferable to speak of word form or some other such term:
“catch” as a noun and “catch” as a verb are two different words.

If this type of coincidence is found in French it must be very rare if not limited to fairly productive categories of which I can think of only one, and in any case it can in no way approach in number the number of the enormous crop of examples of it that we know is characteristic of the English language.

One of those categories I mentioned: the verbs ending in -er; however they are not much used as they do not feel as natural as other means to express the same thing (the corresponding noun that is). Some of the nouns in that category are established words (in the dictionary) while others that are not can still be used.

parler (rather written language), manger, coucher, aller (very common that one), déjeuner (also very common), etc

restricted free productivity: acceptable for certain verbs (the principle is not clear to me); example:

• Pour ce qui est du gratter il n’y a pas de problème, c’est le polissage qui est difficile.

Oui, c’est commun mais tu n’as précisé la forme du verbe qui t’intéresse.

En français il est assez courant de nominaliser le participe présent des verbes. (e.g habiter -> participe présent habitant -> nom habitant). Le substantif est alors rigoureusement identique au verbe pris au participe présent.

Mais je présume que tu ne parles que de la nominalisation de l’infinitif.

Formellement il est toujours possible d’utiliser un infinitif comme nom. On parle de nominalisation par dérivation impropre ou décatégorisation. (manger, toucher, boire, penser, vivre…) mais on ne rencontre ces formes que dans des ouvrages spécialisés sur le sujet précis et toujours et exclusivement au singulier précédé de l’article le.

Utiliser un infinitif en tant que nom était une pratique courante en ancien français.
Cette substantivation a disparu en français contemporain. (Alors qu’elle est restée vivante dans les autres langues romanes).
On a néanmoins gardé de cette époque les mots qui étaient entrés dans l’usage, à commencer par les verbes auxiliaires ou semi-auxiliares (être, avoir, devoir, pouvoir…)

On lira avec intérêt sur le sujet le travail de Claude Buridant.

The infinitive-based deverbal nouns the other answers mentioned aren’t very productive anymore except in some specific registers, mostly scholarly works of philosophy and psychology. That is, nouns like le manger, le parler or le coucher started being used during a previous stage of the language and are now part of the French lexicon, but speakers are rather unlikely to spontaneously create a new word like “le fumer” for the action of smoking, for example.

Part of the reason is that the infinitive, originally a type of deverbal action noun, has been becoming since pre-Latin times more and more verb-like in usage, eventually losing almost completely its availability as a noun.

The other answers concentrated a lot on the infinitive, but unlike the English infinitive, the French is marked by a suffix. There is however a verbal form that’s phonologically a bare stem: the singular indicative present.

And as it happens that it’s very common for the bare root of first group verbs to be used as an abstract noun, and this process is fully productive, creating nouns phonologically identical to verb forms.

Following the model of well established vocabulary items like:

• Avancer -> l’avance (to advance -> the advance)
• Danser -> la dance (to dance -> the dance)
• Tremper -> la trempe (to drench or soak -> the mettle (from the action of soaking red hot metals in water, which affect the quality of the metal)
• Laisser -> la laisse (to let -> the leash)
• Marquer -> la marque (to mark -> the mark)

Speakers coin new nouns all the time:

• Aguicher -> l’aguiche (to seduce -> the act of aggressively teasing)
• Gagner -> la gagne (to win -> the win)
• Vaper -> la vape (to vape – ?the vaping)
• Bouffer -> la bouffe (to eat -> the food) (first attested in print in 1921!)

The existence of another noun of the same meaning inhibits the creation of those suffixless deverbal nouns, but doesn’t block it completely, as exemplified here by la gagne, whose birth wasn’t completely stopped by la victoire (it’s however, at least for now, used in a lot less contexts than victoire).

As you’ve probably noticed, those nouns are all feminine. There existed old suffixless masculine deverbal nouns like porter -> le port or chanter -> le chant, but they aren’t productive anymore, probably because sound changes like the loss of the final /t/ of those words have muddled the etymological link in speakers’ minds.