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SHAREOWNERS' EQUITY (Details) (USD $)
In Millions, except Share data, unless otherwise specified
12 Months Ended
Jan. 03, 2015
Dec. 28, 2013
Dec. 29, 2012
Mar. 30, 2013
Equity [Abstract]        
Common shares, authorized (in shares) 65,000,000us-gaap_CommonStockSharesAuthorized 65,000,000us-gaap_CommonStockSharesAuthorized    
Common shares, par value (in dollars per share) $ 0.10us-gaap_CommonStockParOrStatedValuePerShare $ 0.10us-gaap_CommonStockParOrStatedValuePerShare   $ 0.10us-gaap_CommonStockParOrStatedValuePerShare
Stock repurchased and retired during period, value (in dollars) $ 9.0us-gaap_StockRepurchasedAndRetiredDuringPeriodValue $ 2.8us-gaap_StockRepurchasedAndRetiredDuringPeriodValue $ 10.0us-gaap_StockRepurchasedAndRetiredDuringPeriodValue  
Stock repurchased and retired during period, shares 243,020us-gaap_StockRepurchasedAndRetiredDuringPeriodShares 88,200us-gaap_StockRepurchasedAndRetiredDuringPeriodShares 400,000us-gaap_StockRepurchasedAndRetiredDuringPeriodShares  
Shares retired that had been previously granted as stock awards to employees, but were forfeited upon not meeting the required restriction criteria or termination (in shares) 68,675fele_SharesRetiredThatHadBeenPreviouslyGrantedAsStockAwardsToEmployeesButWereForfeitedUponNotMeetingRequiredRestrictionCriteriaOrTermination 6,190fele_SharesRetiredThatHadBeenPreviouslyGrantedAsStockAwardsToEmployeesButWereForfeitedUponNotMeetingRequiredRestrictionCriteriaOrTermination 16,712fele_SharesRetiredThatHadBeenPreviouslyGrantedAsStockAwardsToEmployeesButWereForfeitedUponNotMeetingRequiredRestrictionCriteriaOrTermination  
Shares retired that were received by employees as payment for the exercise price of their stock options and taxes owed upon exercise of their stock options and release of their restricted awards (in shares) 40,679us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation 273,799us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation 419,208us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation  
Increase in shareowners' equity as a result of stock options exercised (in dollars) 2.3us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised 5.1us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised 4.7us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised  
Accumulated other comprehensive income (loss), currency translation adjustment (in dollars) (51.8)us-gaap_AccumulatedOtherComprehensiveIncomeLossForeignCurrencyTranslationAdjustmentNetOfTax (16.0)us-gaap_AccumulatedOtherComprehensiveIncomeLossForeignCurrencyTranslationAdjustmentNetOfTax    
Accumulated other comprehensive income (loss), pension liability adjustment (in dollars) $ (56.1)us-gaap_AccumulatedOtherComprehensiveIncomeLossDefinedBenefitPensionAndOtherPostretirementPlansNetOfTax $ (38.7)us-gaap_AccumulatedOtherComprehensiveIncomeLossDefinedBenefitPensionAndOtherPostretirementPlansNetOfTax