Profits will fall if fixed costs (or, for that matter, variable costs) rise. Profits will rise if fixed costs or variable costs fall.
Fixed costs are those costs which do not change regardless of the level of production. For example, a motel has fixed costs because it cost a fixed amount of money to build the motel and those costs (assuming they are still paying off a loan for the building) apply regardless of whether they have any guests in the rooms. Variable costs are costs that change depending on the level of production. With our motel example, the more guests the motel has, the more it has to pay housekeeping and the more money it spends on things like laundry detergent and food for the continental breakfast.
Profit can be defined as the amount to which revenues exceed costs. If you take in more money than you expend in making your product, you make a profit. If costs go down, profits will go up. If costs go up, profits will go down. Therefore, an increase in fixed or variable costs will reduce profits while a decrease in fixed or variable costs will cause profits to rise.