Here is my last paragraph for you to check.

I left out the most important part, which we need to vary, bearing in mind that English must be the lingua franca.
Do you think we should include "helping the pupils overcome their inhibitions" among the linguistic objectives?

I will start with the end of the paragraph which we need to vary.

11) This is why we consider it necessary to familarize pupils with a European and international dimension of working together and improving their foreign language skills.
12) Thus the project and its subject very well fit the pedagocial needs of the three schools, leading to a deeper understanding of the respective European partners.
13) Even though there is no anglophone partner involved, English is the official language of the project. Besides, it is taught at all three schools.
13) WE MUST VARY THIS SENTENCE
The pupils will, however, not only communicate in one foreign language but also in the languages of their partners: Italian, German and French.
(We can say that:
As English has been internationally recognized as the language of science and is taught at all three schools, this language has been chosen as the lingua franca for our project.
During the various exchanges,however, the participating students will have the chance to get to know more about the culture and institutions of their partners. Their mutual involvement will certainly urge them to learn other languages in the future??)
As you know, I need to vary their sentence on the possible use of other languages, which may cause misunderstandings as my students don't study either German or French.
German is taught at the French school along with English)

11) This is why we consider it necessary to familiarize pupils with a European and international dimension of working together and improving their foreign language skills.

12) Thus the project and its subject fit very well into the pedagocial needs of the three schools, leading to a deeper understanding of the respective European partners.

13) Even though there is no British <~~this could also be "English-speaking" or "predominantly English-speaking" partner involved, English is the official language of the project, primarily because it is taught at all three schools.

13) WE MUST VARY THIS SENTENCE
The pupils may also communicate in the languages of their partners: Italian, German, and French.

(We can say that:
As English has been internationally recognized as the language of science and is taught at all three schools, this language has been chosen as the lingua franca for our project.

During the various exchanges, however, the participating students will have the chance to get to know more about the culture and institutions of their partners. Their mutual involvement will certainly encourage them to learn other languages in the future.)

Do these variations above work?

To vary the sentence, you can consider the following options:

1) In addition to English, the pupils will also have the opportunity to improve their language skills in Italian and French, which are the languages of their respective European partners. However, since German is not taught at any of the three schools, it may result in potential language barriers and misunderstandings during the exchanges.

2) As English is the lingua franca for our project, the pupils will primarily communicate in this language. However, to foster a deeper understanding of their European partners' cultures, they will also have the chance to learn basic phrases in Italian and French. It is important to note that German, although not taught at any of the schools, can still be a valuable language for future exchanges and collaborations.

3) While English serves as the official language of our project, the pupils' engagement with their European partners will allow them to explore other languages, such as Italian and French. Although German is not part of their language curriculum, efforts can be made to provide additional resources or language support to students who are interested in learning it alongside English.

Remember to choose an option that aligns with your students' language abilities and the resources available to you.