Link to full text in English:

http://www.gutenberg.org/files/467/467-h/467-h.htm

Link to full text in French:

http://gallica.bnf.fr/ark:/12148/bpt6k575827/f1.image

Link to full text and some excerpts in French (a great site if you want to work with a few key excerpts, also has vocabulary and reading notes):

http://lettres.ac-rouen.fr/francais/tendre/cleve1.html

Link to La Princesse de Clèves by Lafayette: A New Translation and Bilingual Pedagogical Edition for the Digital Age:

https://www.fulcrum.org/concern/monographs/cc08hj19v