You should not worry about the university so much as worry about your organization's personnel manager and your own record for hiring good staff.
Most EU countries have employment law stating that positions (part- or full-time) must be fairly advertised internally, locally and nationally prior to their being offered internationally - though in exceptional cases like rare skills they may be advertised nationally (e.g. national newspaper) and internationally (e.g. New Scientist) simultaneously.
The jobs at issue here are either summer/sandwich internships or else graduate-level trainee positions. It's possible existing staff at the employer organization may have sons/daughters who would be candidates for such jobs - you cannot afford to vex these staff by denying their children their right to apply. Then there are student/graduate candidates from other local or national colleges who also have a right to apply - though naturally the non-locals would be disadvantaged if they have to live away from home.
Now, there's nothing wrong with inviting students to apply for jobs at your organization as long as they are aware that they are not the sole candidates and appointments are made on broad merit grounds.
But the dilemma you face is here. On the one hand, if you do right educationally and not mention jobs till the end of the course/exams then you stand to miss some of the students you'd like to hire - they may have committed to working elsewhere, going abroad, etc in the meantime. On the other hand, if you advise all (and it must be all to avoid accusations of "creaming" being made to university management) students of possible internships/jobs, then this will affect both student motivation and cooperation between students - some students will cut the professional/social throats of others just for a job, it's a fact.
Personally, I think the best thing is for you to keep silent on jobs till after your educational commitment is complete but occasionally (at suitable points of lectures or in discussing course work) making the point that employers generally like certain virtues in candidates like cooperation with people you may not like socially, willingness to give some extra time to a sticky problem, initiative, honest endeavour, thinking outside the box, good design, clear communication, appreciation of human diversity, etc, etc. The real good ones will take some of this aboard, the what's-in-it-for-me types will turn a deaf ear.
I think that this approach - despite the risk of losing an occasional coveted candidate - is fairest to the employing organization, the student candidates, the university's reputation and - eventually in the long run - your own judgement and reputation.
Note too that those who shine in a university environment may not stand out so much in other working environments: they may be less motivated in an all-ages situation, or may find the stop/start tempo hard to take or may not be motivated by working for the company's reputation instead than their own. Were you to proceed hastily and unilaterally "book" a student for an internship where he/she disappoints then some people in your own company will note this - formally and informally.