This can be achieved easily if you are using PostgreSQL 9.0 and above through the unaccent contribution (http://www.postgresql.org/docs/9.0/static/unaccent.html).

Install the unaccent contribution by running the unaccent.sql script. For Ubuntu users, this file is located at /usr/share/postgresql/9.0/contrib/unaccent.sql

Connect to your database and run the following instructions:

CREATE TEXT SEARCH CONFIGURATION fr ( COPY = french );
ALTER TEXT SEARCH CONFIGURATION fr
    ALTER MAPPING FOR asciihword, asciiword, hword_asciipart, hword, hword_part, word
    WITH unaccent, french_stem;

Then replace in your default-repository-config.xml file the french analyzer by the one you just defined (fr in this example).

If using Postgres 8.4, you can find in the documentation the instructions to build the unaccent module: http://doc.nuxeo.com/display/ADMINDOC/Configuring+PostgreSQL#ConfiguringPostgreSQL-Accentinsensitivefulltextsearch