I just bought a new chainring. 51t ta specialites french 144bcd.

My problem is that on the front side of the ring where it says the name brand and the measurements, the bolt circles have a groove/cup that the bolt cap goes into maybe .5mm and I can't tighten the bolts tight enough. I had to flip the ring around because the backside had no groove/cup and the bolts were able to get tight.

is this safe? or should I just look for shorter bolts? The bolts I have now are single ring bolts. Thanks.

You will be fine. The cup is there for pure aesthetics.