I need records of telephone conversations (or simple conversations between two persons) with their transcripts. I need English and French datasets.
Most telephone recording datasets are privately owned by parties who have access to such data like for example call-centers and tech-support companies etc. This data is subject to various privacy laws (which differ from one country to another), therefore it is tricky to find such data.
Nevertheless, the CallHome database and the CallFriend database -by TalkBank- seem to fit your requirements. Furthermore, TalkBank provides a variety of datasets with support for different languages. The full list can be found here.