What is the proper English term for polycopié (de cours)?

In my experience in the US, this is typically called a handout, or it is referred to informally in class by the name(s) of the author(s) or a short title. Yes, that means that "handout" can be anything from a single, informal sheet passed out occasionally to a bound book (which is typically not available through other channels, etc., it might be written by the prof and be otherwise unpublished).

Sometimes such material is referred to as lecture notes, as well. And there is probably a certain amount of variability wrt geography, course level, etc.

I would suggest trying to find out what term is used by the target use case: if you are preparing something for a course presented in English, ask those involved with teaching it or designing the curriculum, etc.

IMO, the binding used, if any, is of less importance than the content. No one really cares much whether something is tape-bound, spiral-bound, or whatever.

In general, they can be called softbound books. (or booklets) (or copy/copies)

softbound (adj.): Not bound between hard covers

_{Note: softbound is used as "soft bound" or "soft-bound" as well.}

"bound copy" is also used in universities, especially for thesis submissions. It is a more general term that can cover copies bound with different type of soft binding styles.

More specifically, there is spiral-bound (or coil-bound). The binding technique is called coil binding or spiral binding.

spiral-bound: of a book : having pages held together along one edge by a continuous piece of wire or plastic that passes through holes in the pages

_{~ Source: http://cios233.community.uaf.edu/design-theory-lectures/all-about-paper/}

There is "comb-bound" also (made with comb binding technique)

_{~ Source: http://en.wikipedia.org/wiki/File:Comb_bind_examples.JPG}

A course-pack is a collection of articles or other documents, selected by a professor for use in place of (or sometimes in addition to) a textbook for a course, and usually bound in one of the ways described by ermanen.