I searched through the Paris birth records and found two Buchers born in 1888 but neither was the right one. There were some born in the year before and after. Is 1888 firm and do you know the birth date? Was the child a boy or girl and do you know what it's birth name was?
I searched the Paris death records from 1893 to 1912 and didn't find Pauline. She may have lived just outside of Paris so I'll do some searching there.
Fingers crossed I can find something for you.