Thanks for all your answers, information and advices in this research.

They are very appreciated.
I discussed today with my grand mother and have a few more information (but will have more in the following days after having contact with more people involved in the story)
- The February timing looks to be forgotten: it's look that the weather was not cold at this time, most probably in spring or summer.
- You are true about the difficulties about to stay during hours in a cold river. The pilot was ill in the following days. Countrary from what I known yesterday, the pilot didn't left to Paris the following day, but was hidden in a small house in the suburb of Gournay-en-Bray. Unfortunatly the doctor and the owner of the house, who take care of him in secret looks to be dead for a long times. As they spent at least one week with the pilot, they probably had the most details about him.
- The story occured before the month of June 1944: the uncle who hidden the pilot (his name was Pierre Lefaucheux) was arrested by the Germans in Paris, in the beginning of this month, sent in deportation to Germany and only escaped in september, after the area wqx freed.
For the people who have access to information, a few specific details, who could perhaps help:
- The name of the city was, during the war, "Gournay", the end of the name was added after the war. (Gunny: inf fact "en bray" is a reference to "county" where the city is, and not about the name of the river. But you are true that in Europe, different cities have a reference to a river)
- The name of the place where the story occured (the very small town of a few house around the farm, in french we call that a "hameau", I don't found a corret translation) is Mothois, the spelling from google map is incorrect.
- Other close smallest towns ("hameaux") in the area are "Saint Quentin-des-prés", "Hyancourt" and "Laudencourt"
Best Regards
Loïc