I found an instruction manual (perhaps for the same program) that defines the term. It just seems to be the technical term for the action of clicking on the help button.

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Note added at 4 hrs (2017-09-08 14:50:15 GMT)
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Perhaps I should clarify. From what the OP is describing, the software seems to a front-end for retrieving patient records from databases that don't talk to each other. In such systems, it's common to have commands that change function depending on the screen context. For example, on one screen, the 'F12' key might pull up the help menu for the page that you're on. On another, it might retrieve patient records. Clearly, none of us has personal experience with the system in question, but given the available information, "contextual call" seems to be a reasonable inference, and doesn't warrant such a condemnatory response.

https://patents.google.com/patent/US8046358B2/en
For medical imaging data. "In accordance with aspects of the present technique, a method of retrieving information of interest is presented. The method includes parsing data based upon a predefined context definition. Further, the method includes interpreting the parsed data based on the predefined context definition."

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Note added at 4 hrs (2017-09-08 15:18:00 GMT)
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This should fit your context. "Développement et intégration dans notre système d’information hospitalier (SIH) d’outils d’accès à la connaissance et leur appel contextuel ; ce développement devra être effectué en collaboration avec la Direction Informatique et les éditeurs de logiciel de SIH." http://www.chu-rouen.fr/cismef/d2im/

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Note added at 4 hrs (2017-09-08 15:21:27 GMT)
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And the definitions given: https://link.springer.com/article/10.1007/s10115-009-0231-1
"The increasing prominence of information arising from a wide range of sources delivered over electronic media has made traditional information retrieval systems less effective. Indeed, users are overwhelmed by the information delivered by such systems in response to their queries, particularly when the latter are ambiguous. In order to tackle this problem, the state-of-the-art reveals that there is a growing interest towards contextual information retrieval which relies on various sources of evidence issued from the user’s search background and environment like interests, preferences, time and location, in order to improve the retrieval accuracy."

The context is any software, where you are logged in as a specific user, browsing a specific person's or entity's file (typically a client, a patient in my case, etc. [= "the context"]).

From this software A, you want to launch another software B (usually using a button configured to this end). OK, this is the "appel / call" part...
BUT, the "contextuel" part is that once software B is started, it takes you directly to the information for the desired entity / person :
- you do not need to log in in software B
- you do not need to search (using software B\'s search engine) for the entity, it automatically opens on the correct file/record.

this is NOT part of any menu, it's the description (for a presentation) of how some software works.

the point of "l'apppel" is to launch another software in "the context" of some already known pieces of information (patient's ID, whatever)

from I could find "contextual launch" would be the term to use, although "context-based information retrieval" is for sure also correct.