You can write to a company or entity for wich you would like to work but do no currently offer internships or positions.
Your CV may be put in a corner, but if it is interesting, it will probably be retained to remind you later when an opportunity arises.
But be careful: before sending your letter, do not forget to find on their website the contact of the person most concerned by your request! This may be the human resources manager, the person in charge of the department you are interested in, or even the president or director. This will prove to the company or association that you have really been interested in its activities and that you are motivated.
And your application will have more weight!