He vowed to marry a certain girl then he did not fulfil his vow

Firstly: 

What the Muslim should do is avoid making vows, because the
Prophet (peace and blessings of Allaah be upon him) told us not to do
that. 

Al-Bukhaari (6608) and Muslim (1639) narrated that Ibn ‘Umar
(may Allaah be pleased with him) said: The Prophet (peace and blessings
of Allaah be upon him) told us not to make vows and said: “They do not
change anything, rather they are a means of making the miser give
something.” 

See also question no. 32724 and
36800. 

Secondly: 

The scholars (may Allaah have mercy on them) stated that vows
are of several types, such as a vow that is intended as an oath, which is
aimed at encouraging an action or avoiding it. 

The ruling on such vows if they are broken is that the person
is given the choice between doing that action he vowed to do or offering
kafaarat yameen (expiation for breaking an oath). 

Ibn Qudaamah said in al-Mughni (13/461): 

If a person makes a vow
in the sense of making an oath, to stop himself or someone else doing
something, or to make him do something – such as saying, “If I speak to
Zayd, then I must go on Hajj, or give my wealth in charity, or fast for a
year,” then this is an oath, and the ruling thereon is that he has the
choice between fulfilling what he swore to do, in which case he does not
have to do anything else, or breaking his oath, in which case he has the
choice of doing what he vowed to do or offering kafaarat yameen. This is
called the vow of argument and anger, and he does not have to fulfil it…
This is the view of ‘Umar, Ibn ‘Abbaas, Ibn ‘Umar, ‘Aa’ishah, Hafsah, and
Zaynab bint Abi Salamah. This is also the view of al-Shaafa’i. End quote. 

It seems that your vow to fast for three months if you did
not marry this girl is of this type, because by doing that you intended to
encourage yourself to marry her. This is an oath. 

See also question no. 45889. 

Kafaarat yameen (expiation for breaking an oath) is mentioned
in the verse where Allaah says (interpretation of the meaning): 

“Allaah will not punish
you for what is unintentional in your oaths, but He will punish you for your
deliberate oaths; for its expiation (a deliberate oath) feed ten Masaakeen
(poor persons), on a scale of the average of that with which you feed your
own families, or clothe them or manumit a slave. But whosoever cannot afford
(that), then he should fast for three days. That is the expiation for the
oaths when you have sworn. And protect your oaths (i.e. do not swear much).
Thus Allaah makes clear to you His Ayaat (proofs, evidences, verses,
lessons, signs, revelations, etc.) that you may be grateful”
[al-Maa’idah 5:89] 

See also question no. 45676. 

To sum up: if you marry that girl, then you do not have to do
anything. If you do not marry her, then you have the choice between
fulfilling your vow of fasting for three months, or offering kafaarat
yameen. 

And Allaah knows best.