Crazy_Garry

Так вроде.

def project_document_add(request, id):
    project = Project.objects.get(id=id)
    if request.POST:
        form = DocumentForm(request.POST)
        if form.is_valid():
            form.save()
            return redirect('projectinfo', id)
    org = ProjectCompany.objects.filter(project=project)
    context = {
        'form': DocumentForm(initial={'project': project, 'organization': org}),
        'project': project
    }
    return render(request, 'documents/projectdocumentadd.html', context)

upd:
Я же QuerySet с ProjectCompany выбрал... Надо достать из него Organization...
Так может.

org = [company for company in ProjectCompany.objects.filter(project=project)]
    context = {
        'form': DocumentForm(initial={'project': project, 'organization': org}),
        'project': project
    }