It seems easy to perform by Friedel-Crafts reaction of ArCOCl and furan or 2-methyl furan in presence of AlCl3, but very few examples, low yields, patents etc.
It seems that you need to prepare 5-methyl-2-furyl phenyl ketone. You can follow the reaction between 5-methylfuran and benzoylchloride in presence of anhydrous Stannic chloride in carbon disulfide (anhyd. SnCl4/anhyd. SC2) as solvent at low temperature. Alternately one can try the reaction with 5-methyl-2-furoylchloride with benzene using anhyd. SnCl4 as Lewis acid catalyst at low temperature.
5-methyl-2-furoyl can be prepared via reaction of Na-salt of 5-methyl-2-furoic acid with oxalyl chloride in anhyd. benzene. For this reaction yield is normally not too high but it is expected that yield will be better than that when anhyd. AlCl3 is used.