France has cathedrals in modest towns and basilicas that are not cathedrals at all. The words describe different qualities, and neither one is about size.
A cathedral is defined by administration
A cathedral is the church housing the seat of a bishop, which makes it the administrative center of a diocese rather than the largest church in an area.
Because dioceses were drawn centuries ago around the towns that mattered then, a small town today can hold a cathedral while a larger neighbor does not.
When a diocese is merged or moved, the title can survive in a former seat, which produces towns with cathedrals and no resident bishop.
A basilica is an honorific
The title of basilica is conferred as a distinction, typically on a church of particular significance as a place of pilgrimage or historical importance.
It carries certain ceremonial privileges but no administrative function, and it can be granted to a church of any size.
A building can be both, holding a bishop's seat and carrying the honorific, which is why the terms are sometimes used interchangeably in error.
Ownership in France is unusual
Church buildings that predate the separation of church and state are owned by the state or by the commune, while the religious use continues.
That is why restoration of a famous cathedral is a public works matter and why maintenance quality varies with municipal budgets.
Buildings constructed after that separation are owned by the church itself, which produces two quite different funding situations across the country.
Entry rules follow from that ownership
Most French cathedrals and parish churches are free to enter, because they are public buildings in active religious use rather than attractions.
Charges usually attach to specific parts, such as a tower climb, a treasury, a crypt or a cloister, which are managed separately.
Abbeys and monastic sites that no longer function religiously are more often run as monuments with paid admission and fixed visiting hours.
Reading the building itself
Construction over centuries left most large French churches with mixed styles, and a rounded arch beside a pointed one usually marks a building phase rather than a design choice.
Later restoration campaigns added elements in a style imagined to be medieval, so not every gothic detail is old.
Nave height rather than floor area is the clearest indication of ambition, since raising the vault was the difficult and expensive part of the work. Collapses during construction were common, and several French cathedrals were rebuilt after one.