Quran does not define a certain place to pray, but requires Muslims to make certain places mosques in order to meet the social needs. Legally, everywhere on earth is free for praying as long as the place is clean enough.
There is no problem for Muslims to pray in a church as long as its authorities permit it. But it wouldn’t be the way of the Messenger. Finding a mosque should be better, or converting a place to a mosque if there is a lack.
Naming a place as a mosque or a church is an issue about public administration. Muslims do not have to bother with the official status of the building they are praying in.
Now, let us consider the subject from the side of Christians.
If we are required by a group of Christians to pray in a mosque, we cannot prohibit them. But we have a right to ask them not to do their prayers by disturbing the regular prayers of Muslims. They can choose the free times in between. Historical resources indicate that the Prophet gave permission to a group of Christians from Najran to pray in the mosque of Madina.
There are also some sects like Syriac Christianity who follow the authentic style of praying that involves bending and prostrating like Muslims. There is also no reason to prevent them from praying even in the same line with Muslims, if they ask so. We know from Quran that Muslims and Jews were praying in the same place together in Madina (facing Mizrah) until the verses that command the change of Qibla were revealed.