A database produced by the Modern Language Association of America which provides bibliographic citations and much full text for a vast number of journal articles and other sources in literature, language, linguistics, and folklore. Many languages are represented, including French, with coverage from 1926 to the present. 

Academic Search Complete

A scholarly database providing full-text journal coverage for nearly all academic areas of study, including social sciences, humanities, education, computer sciences, engineering, language and linguistics, arts & literature, medical sciences, and ethnic studies. Full text for thousands of publications, with coverage dating back to 1975. 

JStor
A full-text database of journal articles from a large number of disciplines; provides backfiles of whole runs of many important journals in numerous fields. 
Caution: JStor is very popular. However, since its specialty is backfiles, it may not provide current issues of the journals you need. Thus, do NOT limit yourself solely to it when searching for articles.

Project Muse

A database providing full-text access to scholarly journal articles and to other scholarly resources in the arts and humanities, social sciences and mathematics.