The basic principle that we have stated in numerous fatwas is that it is not permissible for a woman to travel without a mahram, whether the trip is for an act of worship such as Hajj, or to visit her parents, or it is a permissible kind of journey for other purposes. 

This is indicated by the texts and common sense. For example: 

1-

The Prophet (blessings and peace of Allah be upon him) said: “No woman should travel except with a mahram and no man should enter upon her unless she has a mahram with her.” A man said: O Messenger of Allah, I want to go out with such-and-such an army, but my wife wants to go for Hajj. He said: “Go with her.”

Narrated by al-Bukhaari, 1862 

Muslim (1339) narrated from Abu Hurayrah (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) said: “It is not permissible for a woman who believes in Allaah and the Last Day to travel the distance of one day, except with a mahram.” 

And there are many hadeeths which speak of the prohibition on a woman travelling without a mahram; they are general in meaning and include all kinds of travel. 

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Because travel usually causes exhaustion and hardship, and because women are weak and need someone to look after them and stay with them, and things may happen in the absence of her mahram that she is not able to deal with. These are things that are well known and are frequently seen nowadays because of the large number of accidents involving cars and other means of transportation. 

Moreover, if a woman travels alone she may be approached and tempted to do evil, especially when there is a great deal of corruption. Someone may sit next to her who does not fear Allah and he made may doing haraam actions seem appealing to her. It is perfectly wise that the woman should be accompanied by her mahram when she travels, because the purpose of having her mahram present is to protect her and look after her. Travelling is a situation in which emergencies may arise, no matter what the length of the journey is. 

An-Nawawi (may Allah have mercy on him) said: To sum up, everything that may be called travel is forbidden to women without a husband or mahram. End quote. 

More than one of the scholars have narrated that there is consensus among the fuqaha’ that women are not allowed to travel without a mahram, except in exceptional cases. 

Al-Haafiz Ibn Hajar (may Allah have mercy on him) said: al-Baghawi said: They did not differ concerning the fact that women are not allowed to travel for purposes other than the obligation (the obligatory Hajj) except with a husband or mahram, apart from a kaafir woman who becomes Muslim in dar al-harb (non-Muslim territory) or a female prisoner who is released. Others added: or a woman who becomes separated from her travelling companions and is found by a trustworthy man; in that case it is permissible for him to accompany her until he brings her back to the group.

End quote from Fath al-Baari, 4/76 

With regard to a woman travelling for the obligatory Hajj without a mahram, the scholars differed as to whether this is permissible. The correct scholarly view is that it is not permissible. This has been discussed previously in the answer to question no. 34380. 

This is the basic principle concerning this matter: a woman does not have the right to travel without a mahram and she must be accompanied by a mahram throughout the journey; it is not sufficient for her husband to bring her to the airport and for her father to meet her in the other country. But when there is a case of necessity, there is nothing wrong with it, because necessity makes permissible things which are ordinarily not allowed. 

Based on that, if obtaining French nationality will relieve your friend’s wife of considerable hardship, and it is not possible for her mahram to accompany her on her journey, then there is nothing wrong with her travelling on her own in the manner you describe, just as there is nothing wrong with her obtaining this nationality. 

Shaykh Ibn Jibreen (may Allah preserve him) was asked: What is the ruling on a woman travelling on her own by plane for a reason, with her mahram taking her to the airport and another mahram meeting her at the other airport? 

Answer: 

There is nothing wrong with that if it is too difficult for the mahram, such as her husband or father, if the woman has to travel and the mahram cannot accompany her. In that case there is nothing to prevent that on condition that the first mahram takes her to the airport and does not leave her until she boards the plane, and he contacts the country to which she is headed and makes sure that her mahrams there will meet her in the airport, and he tells them the time of arrival and the flight number. That is because cases of necessity have their own rulings. And Allah knows best. May Allah send blessings and peace upon Muhammad and his family and companions. 

End quote from Fataawa Ibn Jibreen. 

See also question no. 14235 

And Allah knows best.