How serious is saying "Je t'aime"?
Serious.
Did the Serge Gainsbourg song Je t'aime…moi non plus change the meaning of the phrase je t'aime?
No, je t'aime has the same meaning it still has today in that song. The moi non plus line reflects the particular relationship between the lovers, asymmetrical and/or with ups and downs.
If I recall correctly, before the Jane Birkin version was released in 1969, it was not a strong statement, and meant more like Je t'aime bien does today.
No, it was already a strong statement in 1969, as it has been for many centuries.
Back in those distant days it took some flowers to get the message across.
Flowers could complement or substitute the words, but were not obligatory.