He had intercourse with his wife when the muezzin was giving the call to Fajr prayer

Firstly: 

If the muezzin gives the call to prayer as dawn is breaking, then it is obligatory to refrain from things that break the fast from the break of dawn until the sun sets. So once the muezzin says Allaahu akbar, you have to refrain from eating, drinking, having intercourse and everything that breaks the fast. 

Al-Nawawi (may Allah have mercy on him) said: If dawn breaks and a person has food in his mouth, he should spit it out, and if he spits it out then his fast is valid, but if he swallows it then he has broken the fast. If dawn breaks and he is having intercourse but he stops immediately, his fast is valid. But if dawn breaks and he is having intercourse and he knows that dawn has broken, but he continues having intercourse, then his fast is invalidated. No difference of opinion concerning that is known among the scholars. And he has to offer expiation for that according to our view. End quote from al-Majmoo’ (6/329). 

He also said (6/333): We stated that if dawn breaks and a person has food in his mouth, then he should spit it out and complete his fast, but if he swallows it after he knows that dawn has come, his fast is invalid. There is no difference of opinion concerning this, and the evidence for it is the hadeeth of Ibn ‘Umar and ‘Aa’ishah (may Allah be pleased with them) according to which the Messenger of Allah (blessings and peace of Allah be upon him) said: “Bilaal gives the adhaan at night, so eat and drink until Ibn ‘Umm Maktoom gives the adhaan.” Narrated by al-Bukhaari and Muslim. In al-Saheeh there are many similar hadeeths. End quote. 

Based on that, if the muezzin in your neighbourhood gives the call to prayer when dawn breaks, then you have to stop having intercourse as soon as you hear the first takbeer of his adhaan. 

If you know that the muezzin gives the call to prayer before dawn breaks or you are not sure whether he gives the call before dawn breaks or after, then you do not have to do anything further, because Allah has permitted us to eat and drink and have intercourse until the dawn comes. Allah says (interpretation of the meaning): “So now have sexual relations with them and seek that which Allaah has ordained for you (offspring), and eat and drink until the white thread (light) of dawn appears to you distinct from the black thread (darkness of night)” [al-Baqarah 2:187]. 

The scholars of the Standing Committee for Issuing Fatwas were asked: What is the ruling on one who completes his sahoor and drinks water at the time of the adhaan or one quarter of an hour after the adhaan of Fajr? 

They replied: If the person mentioned in the question knows that this is before dawn appears, then he does not have to make up the fast, but if he knows that it is after dawn appears, then he does have to make up the fast. 

But if he does not know whether his eating or drinking came after dawn appeared or before, then he does not have to make up the fast, because the basic principle is that it is still night. But the believer should be careful about his fast and should refrain from things that break the fast when he hears the call to prayer, unless he knows that this call comes before dawn. End quote. 

Fataawa Islamiyyah, 2/240 

Secondly: 

If you were unaware of this ruling and you thought that abstaining was only required after the end of the adhaan, then you do not have to offer any expiation, but you should make up that fast in order to be on the safe side, as well as repenting and seeking forgiveness for your falling short in learning what is required of you in your religion. 

See also the answer to question number 93866 and 37679. 

And Allah knows best.