I had a look at the French site you provided. I see a number of problems:
1. It is not very detailed. For instance, it requires a sonata movement from Beethoven, Haydn, etc. However both Beethoven and Haydn have composed sonatas with huge differences in difficulty. Some are beginner pieces, some are virtuoso pieces that scare away even the most seasoned performer. Likewise with Czerny etudes (some of which are for total beginners and some which are very challenging), Scarlatti sonatas and so on.
2. This is an exam. It is not enough to know the pieces. You must also know the exam format. Although we can give you some limited help in regards to pieces, only a person familiar with the exam itself can help you prepare for it. Unfortunately this means a teacher – not any teacher – but a teacher who is familiar with the exam.
3. It is also not clear what they mean by a “program of scales”. On an ABRSM exam there are specific scales that you have to know for each grade. The performance requirements are also specific to each grade (how fast to play them, hands together or separate or both; parallel movement, contrary movement or both; over two, three or four octaves). The ABRSM syllabus is very detailed and gives directions to all of these issues. Even then, a teacher familiar with the ABRSM would save a lto of time and anguish. However , if you look at the Guildhall exam, or the Trinity exam, although similar in their requirements, they are quite different in little details. For instance, ABRSM does not care which fingering you use on scales – as long as it sounds good – while Trinity demands a specific fingering. This is not obvious and again a teacher with experience in the exam format will save you a lot of time.
So I would suggest as a first step that you contact the administration of this school and ask for the following details:
i. Difficulty of the pieces. Do they have suggestions? You see, there I no point in preparing Beethoven’s sonata Op. 49 no. 2 – the easiest of the 32 – if they are expecting something on the level of the Pathetique (sort of halfway the difficulty scale). Likewise, there are 555 Scarlatti sonatas. Some are for total beginners some are pieces of the highest virtuosity. Again, there would be little point on preparing K32 (one of the easiest) when they are expecting K141 or similar (one of the most difficult).
ii. Find out about the scales and the requirements. Is it your choice? Only major and minor scales, or are there chromatic, whole tone and pentatonic scales as well (and others)?
iii. There is also sight-reading. What is the level? Can they give you an example of piece that you may expect to sight read?
Come back once you have a bit more definite information.
Is it possible? I don’t know, you will have to try and tell us later. (But without a teacher it will be hard). If you are still alive, there is hope.

Best wishes,
Bernhard.