Roman Catholic Churches in France have not used the Rite of Lyon on a regular basis since the 19th century. I think there may have been a one-off liturgy in Lyon, but there hasn't been regular celebration. There was, I believe, a "Gallican Mass" at the recent ROCOR Western Rite conference.
The Ambrosian rite is in use mainly in the Archdiocese of Milan in Italy.
Some of the (modern) Ambrosian books can be found
here [
unipiams.org].
There's been
many Ambrosian rite related posts on the web site New Liturgical Movement [
google.com].
A Mozarabic ordinary
can be found here [
sanctamissa.org]. The rite was reformed after Vatican II. I haven't examined it to see if this is the pre-reform version or not.
It is not widely celebrated nowadays.
Wikipedia says [
en.wikipedia.org]:
The Mozarabic Rite is celebrated daily in the Corpus Christi Chapel (also called the Mozarabic Chapel) in the Cathedral of Toledo. In Madrid Mozarabic or Gothic Rite is celebrated in Spanish every Tuesday (PÂș Recoletos 11 Monastery of Poor Clare Sisters, 19' 00 h). Two of the original six "Mozarabic" parishes of Toledo remain. About two hundred families in Toledo belong to these parishes and form an association of those who can claim that their families have always belonged to Mozarabic Rite. Additionally, all the churches of Toledo annually celebrate this rite on the Mozarabic Feast of the Incarnation on December 18, and on the feast day of Saint Ildephonsus on January 23. The rite is also used on certain days each year in the Talavera Chapel of the Old Cathedral of Salamanca and less regularly in other cities in Spain. Pope John Paul II celebrated it once in each of the years 1992 and 2000.
I don't know anything about the "Celtic Rite".