France is a predominantly Catholic country, and the veneration of Mary has always been a powerful constant throughout Catholic history. France isn't alone in this; churches dedicated to Mary can be found throughout Catholicism, from Portugal (Nossa Senhora) to Italy (Santa Maria), Germany/Austria (Unsere Liebe Frau) and Poland (Najświętszej Maryi Panny) and beyond, and under many different names - you've got the simply "Mary" or "Our Lady", the many honorifics bestowed upon her (Mother of God, Blessed Virgin, Queen of Apostles...) or a certain feast or theological idea connected to her (Assumption of Mary, Heart of Mary, Nativity of Mary...)

Catholic churches are always dedicated to either a saint or a theological "mystery" (Trinity, Holy Cross, Heart of Jesus, Assumption of Christ etc.). It needn't be a single saint or mystery - Peter and Paul or Cosmas and Damian are popular saintly pairs, but my hometown's pilgrimage church is dedicated to Our Lord's Rest, the Three Wise Men and the Seven Sorrows of Mary at the same time, for example. The dedication of a church or chapel normally follows the dedication of its main altar, but this isn't a necessity - said pilgrimage church's main altar is only dedicated to the Three Wise Men and the other two dedications originally belonged to side altars and only later were transferred onto the entire church. Dedications also can change over time, although in most cases the existing dedications have remained unchanged since the 15th century or so.

Dedications are a fascinating topic for church historians because they can tell us a lot about the history of whatever church you are looking at. Dedications weren't random, but followed specific patterns (even though those patterns are notoriously hard to nail down). One easy example is that churches belonging to the monastery of St Gall in Switzerland would disporoportionately often also carry that saint's name. Specific saintly cults were especially popular during a certain timeframe, so if a church is dedicated to St Anne chances are that it was built during the 15th or 16th centuries, whereas St Joseph massively grew in popularity first during the 17th and 18th centuries in Austria and Bavaria and then during the 19th and early 20th centuries throughout Catholic Europe. Churches dedicated to St James the Elder often lie along pilgrimage routes towards Santiago de Compostela in Spain; dedications to St Afra mean that the church is either situated within the diocese of Augsburg or that there is another connection to said diocese; St Martin's and St Peter's churches are often quite old, and cathedrals are often (co-)dedicated to Mary, seeing as she is also the "Queen of Apostles". None of these correlations are set in stone, but as I said: they are patterns that can at least serve as additional hints to the careful researcher.

The strong Catholic veneration of Mary is quite old, dating back at least to Late Antiquity. It received a massive boost after the Reformation, when venerating her became a clear-cut sign of religious identity, and again during the 19th century when Romantic ideas of the "perfect mother" met a growing pressure by the emergent nation state on the Church. The first Marian churches in Europe are quite old, see e.g. Santa Maria Maggiore in Rome which dates bacl to the 5th century. During the High Middle Ages many cathedral churches were either built anew with a Marian dedication or added it to their portfolio, and after the Reformation Marian churches were often built along denominational borders as to serve as "border markings", stemming back the tide of Protestant heresy.

Sadly I don't think that there is any international survey of church dedications, so I can't really say with certainty whether France really has more Marian churches than other areas or not. There used to be an online database by the University of Leicester, but that seems to have died a quiet death a decade or so ago.