Gérondif, participe présent and adjectif verbal: three -ant forms

The gérondif takes “en” in front and says how or when something is done: “il est parti en courant”, “en arrivant, j'ai compris”. It has one condition, and it is the one people forget: both actions must have the same subject.

The present participle appears without “en” and often condenses a relative clause with “qui” or another circumstantial relation: “un homme portant un chapeau noir” can expand to “un homme qui porte un chapeau noir”. It is invariable, whether its related noun is singular or plural.

The verbal adjective functions as an adjective and agrees: “une histoire intéressante”, “des travaux fatigants”. Compatibility with intensifiers such as “très” is a useful clue, but its quality function and agreement confirm the analysis.

And there is a spelling trap: a few of them are written differently depending on which they are. “Fatigant” is the adjective and “fatiguant” the participle; “différent” against “différant”. That is not a typo slipping through: it is a distinction made on purpose.

And now what is not an “-ant” form at all: whatever follows a preposition. English puts “-ing” there — “without saying a word”, “before leaving”, “instead of shouting” — and French puts an infinitive. “En” is the only French preposition that takes “-ant”.