Praise be to Allah.
If what you mean is actually inhaling some of the substance of the coffee, then deliberately doing that breaks the fast, because it reaches the brain, and that invalidates the fast according to many of the fuqaha’. Moreover, it is most likely that some of it will reach the stomach, and it gives strength as food does, as described in the question.
It says in Kashshaaf al-Qinaa‘ (2/318): ... or he takes up through his nose oil or anything else and it reaches his throat or brain – and in al-Kaafi it says: or his nose – then his fast is invalidated, because the Prophet (blessings and peace of Allah be upon him) forbade the fasting person to go to extremes in taking water up into his nose (when doing wudoo’). Moreover, the brain is part of the jawf (inside of the body), and whatever reaches it nourishes it, so it breaks the fast, as is the case with the inside of the rest of the body. End quote.
If what is meant is simply smelling the fragrance, without inhaling any of its particles, then this does not break the fast, because the fragrance does not have any physical component,
It says in Fataawa al-Lajnah ad-Daa’imah (10/270):
If someone puts on any type of perfume during the day in Ramadan when he is fasting, he does not invalidate his fast, but he should not inhale incense or ground perfume, such as ground-up musk. End quote.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked: What is the ruling on the fasting person using ‘attar perfumes (perfume oils) during the day in Ramadan?
He replied: There is nothing wrong with using them during the day in Ramadan, or inhaling them, except in the case of incense which should not be inhaled, because it has tangible physical particles that can reach the stomach, namely the smoke.
End quote from Fataawa Ramadan, p. 499.
And Allah knows best.