Here is some new test results.

We redefined these products :

See, on front-end, impossible to see products of companies D-cie (DDDDDD) and E-cie (EEEEEE) .

The default setup of the Public user. We also tried with the Multi-companies thicked, Many allowed companies, etc.

It's clear that Odoo must run in single Database mode. If you don't run Odoo in single database mode, impossible to see all products on the front end. 

réf : http://www.zbeanztech.com/blog/portal-feature-openerp-7

in my file /etc/inid.d/odoo :

DATABASE=mydatabase

function _start() {
    start-stop-daemon --start --quiet --pidfile $PIDFILE --chuid $USER:$USER --background --make-pidfile --exec $DAEMON -- --config $CONFIG --logfile $LOGFILE --db-filter $DATABASE
}

Rules are :

BUT IF I DELETE THE COMPANY OF THE PRODUCT DDDDDD :

I CAN NOW SEE THE DDDDDD PRODUCT ON THE FRONT END. But I don't want to remove the value of the field « company » in our products. We need it.

HOW COULD THE PUBLIC WEBSITE USER SEE THE PRODUCTS DDDDDD and EEEEEE without to remove the value of the field « company » for these two products???

THE ANSWER????

SEE HERE :

THanks a lot to me! Clap! Clap! Clap!