You asked about recommendations for things to do in Paris alone. It may seem obvious, but I think that some museums may have guided sessions in English, and a docent-type walk could be rewarding. Or, if your French is up to it, guided mueum visits in general...

If you are a photography lover, do check the old (not new) Bibliotheque Nationale (near the Bourse) for a current exhibit. They are great, in my limited experience, and also intimate and comfortable surroundings.

I also recommend flea markets as good solitary pursuits. In the Marais, the Village St. Paul is a tiny but fascinating place with antique shops. Quite nice.

Bon Voyage, Debbie in Pittsburgh