Is the continued presence of a young man with a non-Muslim woman, who does not intend to embrace Islam after promising to do so, considered fornication, and does this prevent him from marrying a Muslim woman?

It is forbidden for a Muslim to seclude himself with a non-mahram woman, due to the great harms that arise from it, including: the presence of Satan, his whispers, and his efforts to make them fall into sin. Several noble prophetic hadiths indicate this, such as his (peace be upon him) saying: "No man should seclude himself with a woman unless there is a mahram with her," and his (peace be upon him) saying: "Whoever believes in Allah and the Last Day should not seclude himself with a woman who has no mahram with her, for verily the third of them is Satan."

If this applies to a mere fleeting seclusion, then a Muslim residing with a non-mahram woman is even more strictly forbidden. Such residence becomes prohibited even if she has a mahram with her, unless the residence is spacious enough that neither of them can observe the other. Moreover, for a woman to reside in an independent dwelling from a non-mahram man, even if it is adjacent, it is stipulated that common facilities such as hallways, kitchens, or bathrooms and the like should not be shared.

One must repent to Allah for what has occurred. What happened might be a metaphorical fornication, not a real one. Indeed, Allah accepts the repentance of whoever repents. It is advisable to conceal the sin. It is permissible to marry a chaste Muslim woman; in fact, marriage may become obligatory if one fears falling into forbidden acts.