In your scenario there are two transactions with the same input, i.e. an attempt to double-spend.

If the first transaction is already part of a block in the chain, the second one can not be included in any block on top of that block. Other nodes would reject that new block. A miner could build his new block on top of the last block before the first transaction, but that fork of the blockchain would never catch up with the original chain, unless more than 50% of the networks hashrate also builds on top of it. That's the mechanism preventing double spending.

If the first transaction is not yet part of the blockchain (i.e. 0 confirmations), a miner can choose which one to include in the next block. Choosing the one with the higher fee would be a sensible choice, but I don't know if that is implemented in any client. In that case the first transaction would be discarded, and never become part of the blockchain, since it's effectively the same scenario as above.

So, no, there is no potential for a double spend attack through higher transaction fee.