Actually, at one time record sales were a more significant part of an artist's income, but those days are long gone. It has much to do with how the record companies currently share the revenue, which in my opinion is terribly unfair. So yes, touring is a big source of income for an artist.
Alizée seems to want to remain a "mainstream" artist, so she will tend to stick to the conventional "artist/record company" model of doing business. I think if she lost her ability to be under contract with a major label, she might possibly consider exploring less conventional ways of marketing her music.
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