When the btc prices increases the transaction fees will also rise and I remember way back in December when the btc prices was above 15k the fees for like 0.1 btc was something like 30$+ and now for 1 btc it is just 2.5$
Fees have no correlation with the price of bitcoin...
what @reliable said is not right but in a way there is some correlations between the price and the fees.
for example when price was really low ($10 and lower) the fees in BTC were higher (for example 0.01BTC at some point) but as price went up such fees were unreasonable so they came down. now that price is in 4 digits were paying ~0.00000200BTC as fees.
eg. from 2011 https://www.smartbit.com.au/tx/c0e60912386aefeb6bf6c1b98834cbbb1babc704521057aef27a73631242cbdb