If I want from Hong Kong or Taiwan to go to China every week-end or 3 week-ends per month, can I ?

Hi, I have my girlfriend in China, but it seems complicated to find internship in China cause the Work Visa (Z) is hard to get.
However, as a French, if I find something in Taiwan or Hong Kong, can I get a tourist L multy-entry to go every week-end in China?
If not, can I get a tourist L every week form HK or Taiwan to China or the gouvernment will find it suspicious?