Complacence - complacent - complaisance - complaisant
The pair of adjectives complacent and complaisant (with their related abstract nouns complacence and complaisance) share an origin in Latin (complacere, ~ 'to be pleasing'), but they have slightly divergent meanings in current English. The stress in all of these words falls on the second syllable ('cerm-PLAY-sent, IPA: /kəm ˈplaɪs ənt/ etc), (LPD), although OED (1989) records that the French-derived complaisance and complaisant were pronounced with the main stress (c1891) varying between the 3rd and the 1st syllable. "Walker c1800  has IPA: /kɒm ˈpliː zænt/."
- Complacent, which came directly from Latin, has the general sense of 'pleased with oneself'; according to OED: "Feeling or showing pleasure or satisfaction, esp. in one's own condition or doings; self-satisfied." A synonym in more colloquial language is 'smug'. There are two related nouns, both meaning 'the state of being pleased or satisfied with oneself': complacence and complacency, of which the second may be more common nowadays. The use of either carries some connotations of disapproval.
- Complaisant, which came from Latin via French, has the meaning of '[desiring ] to please someone else'. It has the rather unpleasing connotations of "over polite, flattering, subservient" (Fowler). Less pejoratively, it means 'eager to please' or 'polite'; but the overall feeling is of doing too much to please another person, and probably lose one's self-respect by doing so. The related noun is complaisance, or, rarely, 'complaisancy'.
1Probably a later edition, or impression, of Walker, John (1st ed. 1791) A Critical Pronouncing Dictionary and Expositor of the English Language, which had some 40 subsequent editions.