If I were planning a journey like that I would consult Bradshaw's Continental Railway Guide for the year. In the August 1875 copy that I have found online there is a page here which shows routes from London to Constantinople two of which go via Paris and estimate 8 days for the long route and 5 days for the short one, saying "leaving London on Tuesday evening, arriving at Constantinople on Monday evening.". The routes aren't entirely by land but they are at least routes that someone could have taken at the time.