I think that Qur'an contains internal contradictions. Also Qur'an and Islam rejects that key figure of Christianity was crucified and it denys His divinity and trinitarian doctrine.
Doctrinally they are incompatible, because Qur'an rejects christian trinity and that Jesus( or Isa as they call Him ) was divine, although He is called in Qur'an word of God and some other great titles;
The Qur'an Says ...
Holy, Revelation, Mercy When the spirit of Allah appeared as a full-grown man to the Virgin Mary, he announced that she would have a holy son who would be a revelation to mankind and a mercy from Allah (19:17-21).
No Trinity People of the Bible should not exaggerate but speak only the truth about Allah. The Messiah, Jesus son of Mary, was only a messenger of Allah, his word that he gave to Mary and a spirit from him. So believe in Allah and his messengers and stop saying “three.” Allah is only one. He is too transcendent and majestic to have a son. The Messiah is not ashamed to be a slave of Allah (4:171,172).
The Breath and Spirit of Allah Mary, daughter of Imran, who guarded her chastity, is an example of a good wife. Allah breathed into Mary his spirit (the conception of Jesus) and she testified to the truth (that it was a virgin birth) (66:12).
Preached from the Cradle On the Judgment Day, Allah will question Jesus who will be among the other apostles. Allah will ask Jesus if he remembered how he was strengthened by the Holy Spirit and was made to preach to men in his cradle (to defend his mother’s chastity) and as a man (5:110).
Infant Proclamation As an infant Jesus miraculously spoke and proclaimed that he was a “servant” and “prophet” of Allah who had been given the Gospel. The infant Jesus went on to say that Allah had purified him and commanded him to pray, give alms and obey his parents (19:29-33).
Not the Son of God Jesus is the son of Mary. This is the whole truth which Christians are unwilling to believe. It is degrading to think that Allah would have a son! Allah just commands things to happen and they happen (such as Jesus being born of a virgin) (19:34,35). Those who say that Allah has begotten a son proclaim something disastrous. The sky would crack, the earth split apart and the mountains would fall down if they ascribed to Allah a son. It is beneath his majesty (19:88-92). Those who believe Allah had a son are liars who will be punished (10:68,69). Mohammed was told to say that if Allah had a son, Mohammed would be the first to worship him. It is a falsehood that the Christians will have to answer for on the Judgment Day (43:81-83). Allah has no children or wife in his kingdom (25:2).
Only a Slave When the son of Mary is declared as an example (of the Almighty in human form) the idol worshipers ridicule and dispute as to whether their gods are better or Jesus. Jesus is nothing but a slave on whom Allah gave favor and made him an example (of a prophet) for the Children of Israel. Jesus came with clear miracles and told the people to do their duty to Allah and to obey him. He commanded them to worship Allah, their Lord and his (43:57-64).
Strengthened with the Holy Spirit Jesus, son of Mary, was given power to do miracles and strengthened with the Holy Spirit. Yet, when an apostle comes with undesirable teachings, the Jews get prideful and some they call imposters and others they kill (2:87, 253).
No Savior Everyone (including Jesus) will appear before Allah on the Day of Judgment as only a slave who is alone and without a savior or intercessor (19:93-95).
Supported Torah and Predicted Mohammed Jesus, son of Mary, told Israel that he had come to confirm the Jewish Holy Scriptures which came before him, and to announce that another apostle would come after him named Ahmad (61:6).
His Disciples Some Jews followed Jesus as Allah’s helpers and they were blessed to triumph over their enemies (61:14). The disciples of Jesus surrendered themselves to Allah and the Apostle Jesus. They were believers and witnesses. After Allah lifted Jesus up to himself to free Jesus from the unbelievers, the disciples were blessed. The followers of Jesus will be exalted above the unbelievers till the Day of Resurrection when their denominational differences will be settled (3:55).
Worked Miracles Jesus came with clear signs but he was rejected as bewitched (61:6). By Allah’s permission, Jesus brought a clay bird to life, gave the blind sight, healed lepers and raised the dead to life (3:49).
Crucifixion of Christ The Jews have broken the covenant, denied Allah’s revelations and killed the prophets wrongfully. They speak a tremendous slander against Mary. They also say that they killed the Messiah Jesus, son of Mary and Allah’s messenger. They did not kill him or crucify him. It only appeared that way to them. They did not kill him but Allah took him up to himself (4:155-158). After Allah caused Jesus to die (or ascend without dying) and lifted him up to heaven to free Jesus from the unbelievers, the disciples were blessed. The followers of Jesus will be exalted above the unbelievers till the Day of Resurrection when their disputes will be judged (3:55).
Made a Live Bird from Clay On the judgment day, Allah will question Jesus who will be among the other apostles. He will be asked if he remembered how he was given Bible instruction, wisdom and miraculous power. By Allah’s permission, he fashioned a bird from clay and breathed life into it (to make it live) (5:110).
A Table of Food from Heaven On the Judgment Day, Allah will question Jesus who will be among the other apostles. He will ask if he remembered how, by Allah’s permission, he healed the person born blind, cured the leper and raised the dead. The story will be recounted of how Jesus was allowed to call down a table set with food for his followers (5:110-115).
Denies the Trinity On the Judgment Day, Allah will question Jesus who will be among the other apostles. Jesus will be asked if he told mankind to worship him and his mother as two gods besides Allah. Jesus will strongly deny it (5:116-118).
Jesus Is Like Adam Both Jesus and Adam are special creations by the command of Allah (3:59). (This is an interesting verse because the Qur'an rejects the worship of Jesus, yet Satan was banished to hell because he refused to obey Allah’s command to bow before Adam, the man who was sculpted and brought to life from clay. Satan did not believe Allah would ask him to do something so illogical. The story of Satan is found in 7:11-23, 15:28-39, 18:50.)